Trial By Fire: Kill 10 Ships
There are easy enemies, there are hard enemies, there are friendlies who you can attack. Just pop 10 of em and it's yours.

O.C.D.: Full-explore 10 sectors
Get rid of all the gray fog on the map in 10 sectors and enjoy the +1 Agility.
By my understanding, Speed and Agility are ship stats that act as multipliers on your top speed and acceleration, strafing and turning, with 10 being average and each point above and below that adding or subtracting 10%... I'm not sure about that though.

Near Miss: Leave an Asteroid Rush sector
Trivial in a size 5-6 ship with good shielding, and only a little tricky in a smaller one. Asteroid Rush sectors always lack warp gates, so they will appear isolated on your scanner. The majority of isolated sectors are Asteroid Rush sectors. In these sectors, asteroids will continually fly right to left at high speeds. Tank or dodge em until your warp drive is ready and jump out of there.
Asteroid Rushes also tend to have some decent loot floating around, including spaceships that unfortunately are very likely to get popped before you can grab em. They're also an infinite source of mineable asteroids.

Guardian Angel: Save 10 civilian/proxima/syndicate ships from pirate attacks
When one of those ships is in combat with a pirate, attack the pirate, wait for it to die, do that 10 times. I'm not entirely clear on the exact requirements for these kinds of perks, actually; it seems like I need to pop more than the required number. But this will work, and quickly.

Anaximander: Visit 100 sectors
Jump... jump... jump... jump... jump... You'll get it eventually.

Acquired Wisdom: Reach level 50
Again, you'll get it eventually. Probably the quickest and certainly the easiest way to level is the same way to most quickly gain money. Find two stations in close proximity that sell very high-value goods, such as Gold and Platinum (Proxima stations are most likely to have this, but Civilian and Syndicate are possible as well - Civilian won't give faction discounts though). Then, move all the gold to one station and all the platinum to the other. If their prices are different enough, you'll make a profit doing this. If not, you'll need a bit saved up.
When trade good prices are recalculated (which seems to happen on a game-time clock and happen independently for each station), swap the gold and platinum between stations and make a huge profit in both money and xp. The higher the stacks of trade goods, the cheaper they will be and the more you can move for money, so bring gold and platinum from other sectors here. Make sure the gold and platinum are each stacked in one station when you're done or prices won't be so good next time.
This can also be done with civilian stations, but you can never be friendly+ with them, so trade prices will be worse. Pirate sectors are quite rare and don't accept gold or platinum as often. Syndicate, Venghi and Terran stations rarely, if ever, accept gold and/or platinum.

Fun With Maps: Full-explore a large nebula
A good scanner will make a big difference here. The troublesome part here is finding a large nebula. In my first game I had to jump around quite a bit to find one; in my second I stumbled across one before I even had a jump drive. After that, it's just floating around until it's done, maybe jumping out of a bad fight or two.

Hoarder: 40 stacks in your inventory while flying a (1)Shuttle or (2)Yacht
If you have 20 cargo space (pretty typical at that size) then you can look for 40 different 0.5-ish-size items to fill your inventory, some larger, some smaller. The Hercules and Bolder have 45 and 48 space, respectively, and so can commit an average of more than 1 cargo space to each stack, just collecting a bit of everything.
This isn't what I did. It very specifically requires 40 stacks of things. Purchased Vulcan Ammo will remember which station it was bought from, and because of this conservation of information, it will not combine with Vulcan Ammo purchased from another station. What I did, then, is buy one piece of each type of ammo available from each station I visited until I had the achievement. Missile ammo is the largest, and it's 50 per 1 cargo space. Didn't have to think about the size of my cargo hold or the size of the things I buy, or the price either. Easy.

The Real Space Janitor: Destroy 200 pieces of Junk
Junk is found randomly floating in space. You can pick it up and sell it for a pittance, but achievement calls for it's destruction. You can find the button in your inventory screen. Junk is more common (I think) in higher-population sectors, and comes in larger stacks in higher-level sectors. They can get up to, what, 30? 50? A little more sparse at low levels, but this shouldn't be something you go out of your way for. Just pick up the junk while you're doing other things and end it.

The core strategy for Defender, Battle Rush, Combat Genius and The Perfect Predator is the same - get the +5 dps skill, fill all your weapon slots with crafted 6-burst missiles, fill your cargo with missile ammo. After that, it differs for each achievement.

Defender: 10% of damage and defeat an attack fleet of at least your level
The easiest of these four. Attack fleets can be seen on the galaxy map, even outside your scanner range, as explosions on the sector. These will happen in specific sectors chosen at the start of your game, and these chosen sectors will have attack fleets more than 50% of the time. They may or may not change if an attacked station is destroyed, I don't know.
Anyway, find a sector of your level or higher with an attack fleet. Jump in and shoot them. Stay away from their weapons fire. By the time they reach the station and all die, you should have 10%+ damage on them.

Battle Rush: Kill a boss before level 10
This one is a bit annoying, as it's the only level-limited achievement and those first 10 levels can go very quickly. Enemies with gold stars next to their names are sometimes referred to as bosses, but this achievement actually refers to Ravagers.
Some sectors, decided at the start of the game and mostly dark sectors and nebulas, will have these special enemies, which will always have their level at their sector level +3. They will have giant, intimidating icons that can be seen from anywhere in the sector, and their icon will also appear on the sector details on the galaxy map once you've entered it. They will always drop ancient relics which you can use to upgrade your gear, up to tier 4 (tier 0 = gray, tier 1 = white, tier 2 = green, tier 3 = blue, tier 4 = purple, tier 5 = orange).
Ravagers tend to be bigger and tougher than even other gold-stars, but since they're in big ships they're also slower. Playing keep-away with missile spam will usually do the trick, and ravagers in low-level sectors are relatively easy.
The hardest part is finding a ravager before the near-passive exploration experience puts you over the edge. You may want to jump to 2-3 sectors, reload and repeat if you can't find one. I've always found at least one in sector at or below level 10, but not necessarily in the first group of jump gates - you may need a jump drive to reach one.
On the bright side - those first 10 levels go quickly. If you fail, you're not losing much time if you restart.

Combat Genius: Alone, kill a silver-star 2 levels higher and 2 sizes larger
A lot easier than it may first seem. Get yourself in a ship of size 1 or 2, find a sector at least 2 levels higher than you, faction-controlled and with a warp gate. Warp gate guards are always at sector level, will be silver-star about half the time and can be in ships up to size 4. Either reload until you get an appropriate one or just keep using the warp gate - they'll change each time. Once you find one, blow it up with missiles. If you don't want to attack friendlies, jumping in and out of an enemy sector and dealing with the second guard should be only mildly trickier.

The Perfect Predator: Full-kill 5 larger and higher-leveled ships from stealth in 3 seconds each
Get in a shuttle, a Wolf preferably. The most troublesome part here is actually finding the cloaking device. The first one is item level 22 (and tech level 15), and so can only spawn on stations of level 22 or higher (the number next to their name. They can be a fair bit higher or lower than their sector level.) Enemies can drop items that are higher than their level, but cloaking devices are fairly rare. The items on a station are decided when you first jump into a sector, so you can reload until it has what you want.
Now, cloaking devices don't have energy drain, but they severely reduce your energy generation, so counting your costs here is important. Unequip all your computers, except maybe your combat computer. The lower energy costs helps a lot. Then go to a higher-level sector.
Ships in a sector can spawn at levels much lower than the sector level, so they may not all be appropriate. 4 white 6-burst missiles can kill even a size 3 in one salvo, but mind the projectile speed. You need enough of them to hit to kill the target in 3 seconds after leaving cloak, so get ahead of your target and close to them to minimize travel time. Stationary targets are even better.
All that accounted for, just do it 5 times and you're done. If you fail to kill them fast enough (probably due to projectile speed) just keep going... or could try vulcans or something, I guess.

The Last Starfighter: 80%+ damage to an attack fleet of at least your level
This is where things start getting tricky. You need to deal a lot of damage to the attack fleet before they even reach the station (not so much since it's been nerfed from 90%+). I once again spammed missiles for this, but green Peacemakers this time. I've never been able to buy these though, I've only gotten them as drops from enemies (and almost always green for some reason). They're really good missiles. Hit them hard as you can, run if you need to. Can't give any advice beyond that, I've only done it once.

Tutor: Evolve a crew to Legendary
Pretty straightforward, but takes a while. Stick the highest-quality crew you find in your co-pilot seat, get the capstone of the social skills - Master and Commander - as soon as possible to double their experience gain and you should have it well before level 50.

Genocidal: Kill a civilian/proxima/syndicate station
I kill stations like I kill ships, with missiles. This one will permanently make you an enemy of Proxima and the Syndicate, so you're probably looking at throwing away this game when you're done with the achievement. Or playing as a pirate.

Star Killer: Kill a Venghi station / Traitor: Kill a Terran station
Same deal, kill their station and forever be their enemy. If you're looking to sign up with one, then killing a station of their opposition doesn't really cost you anything.

Sloppy: Turn a station hostile and then retreat, 6 times
I'm not clear if jumping out counts as retreating, or if running away but staying in-sector counts. I did both and it took more than 6 runs. Either way, pretty simple. You might want to get a big ship though, stations can do a lot of damage and often have lasers. It's the only perk that detrimentally modifies your ship stats, with a -1 Agility. You can get rid of this perk by getting any of the station-killing perks.

Aggressive: Kill 3 civilian/proxima/syndicate ships
Pop 3 midgets and you're done.

Marauder: Kill 20 civilian/proxima/syndicate ships
This is the only perk on a timer, you gotta kill 20 of them in fairly rapid succession. This will make you an enemy of Proxima and Syndicate, and the easiest way to get out of that hole is to kill pirate attack fleets that are after their stations. It's also the only way to be an enemy of civilians. 30 minutes later (if you don't kill any more), civilians will be neutral again, but Proxima and Syndicate continue to be trouble.

Temperate: Retreat from 10 combats with civilian/proxima/syndicate ships without damaging them
Also pretty easy. Target them, hail them, extort them until they turn hostile, then run until they lose interest. Make sure you don't have an escort and any gunner crew you have aren't on auto-fire. If you're a pirate, you get this almost automatically by ignoring ships that chase after you, but you'll lose it again when you kill those ships.

Ace: Reach 25 in Space Pilot before any other knowledge
Parked ships do not count toward levelling Fleet Commander; you'll get Space Pilot instead. However, while you have parked ships, you won't benefit from Space Pilot bonuses. Anyway, this and the other exclusive perks in this group will probably take you a couple hours each. No special advice on this one -find and kill ships.

Just Me and the Boys: Reach 25 in Fleet Commander before any other knowledge
Hiring mercs will switch you over to Fleet Commander, and is definitely the fastest way to do so. While a carrier would be thematic, I recommend sticking to a small ship if you're rushing this perk - less equipment needed, faster movement, and small ships can still kill quite quickly.

Techie: Reach 25 in Tech Level before any other knowledge
Since you need to fly around a lot and don't need to shoot anything, starting with a small Children of Terra ship (if you have one unlocked) such as the Phantom may be ideal - you can just engage the built-in cloak to avoid any fights you don't want.

Legionary: 10% damage and kill a station with an attack fleet
I don't like killing stations, so I'm putting this here. It's not hard though. Just have some decent missiles (yes, there are other weapons. Yes, they're good. Missiles are easy-mode if you're not fighting gold-stars that outrun even the fastest ones.) and shoot the station while it's distracted by the attack fleet. Or get a really good ship with really good equipment and do it yourself while an attack fleet is in the system.

Dogfighter: Kill 100 size 1-3 ships of at least your level, while flying a size 1-3 ship
My least favorite one by far. Not because it's tedious, though it is. Not because I have to fly a size 3 or smaller ship, that's fine. How do you find targets? Go to a high-level system with roaming enemy ships, shoot them. There's not gonna be nearly enough of them, they're gonna stop coming, or start coming very slowly. How do you get more? Save, reload. Or jump to another system. But it's gotta be a system with things you want to blow up, so you'd need 2 of them to jump between. See a size 4+ enemy ship? Ignore it, it's not important to you, you want the small ones. How do you know how many ships you've killed? You don't, unless you manually keep a tally. What do you do about the inevitable gank squads? They're gonna slow you down if they're silver/gold. I hope you know how to dodge. Or reload.
The process of getting this one feels so very artificial. In general, this game could use better ways of acquiring steady streams of enemies.
Of course, if you're flying a size 1-3 anyway, then just keep playing and it will happen eventually. Though I'd like some kind of progress-tracking in any case.

Battleship Raid: Kill 5 higher-leveled bosses in a size 1-2 ship (Note: actually ravagers, not just any gold-star enemy)
The hardest one, but not too bad. With the introduction of Railguns I'm pretty sure they'll be the easiest way to do this, but missiles or mine cheese can be rather easy as well.
There are a lot of good class 2 ships - Dragon is generally excellent, and Reapers with extra weapon space adders (Nano Components skill, Dogfighter perk, level 45 Space Pilot) become extremely good. Others, such as Phantoms are quite good as well.
On the other hand, there's no great reason to fly a size 1 ship - they might be a tiny bit faster and smaller than size 2s, but it's not an appreciable difference.
Regardless of that path you take, you'll likely be dealing with marauder gank squads while attempting this, especially if the sector is significantly higher-level (enough for a red number). They'll warp in and make everything harder. Ideally, you'd have a cloaking device - it's the only way to shake them off. Then they can attack the Ravager and maybe make it easier. If you have 5/5 in the Renown skill, they won't attack you unless they're much higher-level.
I don't recommend rushing down early ravagers as fast as you can. Below level 15 or so they might be easier (especially if you find a Theseus Ravager), but very soon you'll outlevel your equipment and it'll be easier to gear up first and then take on high-level Ravagers.
Mines are pretty useless in most cases, but they can be stacked and don't expire. Load up a good mine weapon or two in a size 2 ship (ideally the Reaper for ammo efficiency) and drop mines a bit outside the Ravager's aggro range. Then lure it in and, if it wasn't enough mines, try again.
If you perfectly stack the mines then anything that wanders in will set them all off, but if you spread them just a tiny bit, then they'll only set them off enough to kill them. Do this so gank squads don't waste them all. Also, be aware that mine explosions can damage you and neutrals (such as civilians) can set them off.
Missiles don't need to be aimed, so you can focus on dodging. They don't need to be set up and you don't need to rely on the Ravager flying into them, but since the damage isn't all stacked up you'll need to deal with the Ravager's regeneration, which can get quite high. It's possible you'll run out of ammo as well, even if you fill up completely. You'll want the missiles to be fast as well - starred enemies, including Ravagers, will often outrun slow ones. I recommend crafting the biggest small missile you can and packing it with speed boosters.
Railguns are fast enough to reliably hit and long enough range that you can stay out of trouble well enough. They do use ammo, but are much more cargo-to-damage-efficient than missiles. Currently they can only be crafted, but you'd probably want to do that anyway. They don't need to be great railguns if you're low-level and just trying to get them asap.

Gold Rush: 4 metals from one asteroid
At 29 you'll have access to all the metals from gray asteroids, which will take a few asteroid fields (higher ones take longer to chew through and give geology faster, I think). Then go to a sector with very rich minerals, as shown in the hover-over information. An Asteroid Analyzer 2 or 3 will show the minerals in the asteroids. Find ones with all 4 and pop em until you're done (Each asteroid type has one metal that won't appear on these content lists, and it's the last one on the list on the Geology skill. In the case of gray asteroids, it is silver. It's affected by rare metal chance and can pop out of any asteroid of the right color.)

A True Miner: Mine Iridium
The last one unlocked, at Geology 48. Some crew can give a +Geology bonus, and there's a trait you can pick in character creation for another +2. Get to 48, then just find an asteroid with Iridium and pop it.

Space Janitor: Clear 10 asteroid fields
Bigger ships with more mining lasers will do this quicker.

Hard Worker:
Whether this or Space Janitor finishes first depends on the level of sectors you're clearing, as well as the size of the asteroid fields. Hard Worker will probably finish first?

These are all pretty simple, with the possible exception of Pirate and White Collar. Pick a faction (or two, in the case of White Collar), find their stations, do their jobs until you're honored. Hardly any fuss, doesn't even take much time. Terrans are slightly harder, since their stations are harder to find. Blowing up attack fleets is also a very quick way to gain rep.

In the case of Lone Wolf, you'll need to attack the ships of factions you're getting too friendly with to stay below Honored until level 30. Except Rebels - you can just refuse their quest to avoid their background. I'm not quite sure of what does and doesn't lower your rep here, actually - sometimes I lose rep for killing ships, sometimes I don't. But kill enough of them and it'll work.

In the case of White Collar, you'll need to make 20,000 credits in one trade to finish it. See the talk on the Acquired Wisdom perk if you haven't the slightest idea how to do this.

In the case of Pirate. you're actually going to start out hostile to them, and can't walk into their stations and accept their quests. There's an easy way out of this in the Marauder perk, acquired at game-start or any point after, as it sets you to friendly with them, regardless of your previous rep. But, that makes you hostile to Proxima and Syndicate more-or-less forever, and also civilians for half an hour. That's, what, 80% of stations? And most of the rest are Venghi. You gotta find pirate stations and do their quests, and they're rare.
I recommend finding 5 or so pirate stations, and only after that going for the Marauder perk. Much easier to explore first. Then, accept, finish, turn in all the missions you can find until you're done. Expect to spend a lot of time in hostile territory.

Ships are unlocked for your starting loadout options by getting them in a space station and then swapping to them. Most of them can be bought, and cost is mostly about size and quality from about 4000 credits for a white shuttle to 1.5 million for a blue dreadnought. Factions have their own ship types, which require reputation with the faction to purchase, also depending on size and quality. The Screamer is a Red Skull shuttle that only requires neutral relations, while the Proxima Dominance, Syndicate Sanctuary and Red Skull Cerberus are size 6 dreadnoughts that require you to be allied (and are the only things in the game that require that rep level... besides, apparently, Venghi Large Reactors).
I've also found derelict ships of up to size 5 floating in space, with larger ones being increasingly rarer (well, I might have actually found more yachts than shuttles, but otherwise). Faction ships can be found and unlocked this way as well, though be aware that if you sell them, even to civilian stations, you'll need the reputation level associated with the faction and the ship to re-buy them.

There are three special ships here. The first is the blue (5)cruiser Hephaestus. This one requires travelling into empty space in a dark sector between levels 15 and 25. A Hephaestus will jump on you, and you need to defeat it. This encounter is special in that it won't move, so mines can't work (edit: on further play, this might not be true. It fully stops any time it feels the need to change it's direction, which is any time I move, which is all the time. But, technically, it's not immobile). Once again, missiles are the easy way, though not actually the first way I did this. Then you'll get a quest where you just travel to a level 30+ station to pick it up.
The second is the purple (2)yacht Lacewing, which can only be obtained by getting the Battleship Raid perk. It's +threat effect is actually a +2, twice as much as other such effects. Getting the Battleship Raid perk does not allow this ship to spawn as derelicts or in shops, so it can only be obtained if you start with it.
The third is the purple (1)shuttle Mi-laoshu, which requires luck. It's only found as a derelict. It's supposed to be that only one can spawn per game, and only from debris fields (and the only ship that can be obtained from debris fields), but it seems like occasionally someone will find one as a non-debris field derelict. It's not incredibly rare - if you keep digging through the debris, you'll find one eventually. It's technically a Children of Terra ship, though you don't need reputation with them to re-buy it if you sell it.

Factions also have special equipment that only they sell, and requires friendly or honored rep to buy - and, I think, is only dropped by their ships. Faction equipment usually (but not always) scales better with quality than other equipment. Some notable ones, with their item levels in parentheses (which is the minimum station level that can sell them):
Proxima: Asteroid Analyzer 3.0(23), Heavy Tractor Beam(22), PMC Mobile Refinery(29), Heavy Mining Drone(40; can attack ships with their laser, and attack drones can attack asteroids), PMC Collector Beam(25)
Syndicate: Trader Codex 3.0(23), Large Ion Reactor(30), Syndicate Scanner(17), Impulse Drive Mk.Vs(Basic 33, Heavy 48, Capital 50), Syndicate Expansion Module(31)
Red Skull: Pirate Speed Boosters(Basic 12, Large 28, Capital 34), Pirate Heatsink(15)
Children of Terra: Terran Armor(50), Terran Mantle(49; a cloaking device)
Venghi Ascension: Venghi Heavy Armor(50), Venghi Shield Generators(Basic 20, Heavy 30), Venghi Reactors(Basic 29, Large 46), Venghi Missile Launcer(28)

There's a button in the sector info in the galaxy screen for adding notes, which can be used to keep track of stores and derelicts. Derelicts will remain until you pick them up or they're destroyed (though not always in the exact same spot) unless they pop out of graveyards, as will items that were spawned when you entered the sector, but anything that drops after - from enemies, graveyards, pirate hideouts, etc - will disappear when you leave.

There's a comprehensive spreadsheet (not mine) for ships and most everything else here: https://docs.google.com/spreadsheets/d/109WsyDwjnH6glS_DqOsDA4tI0z-sBVLGDQEHnYg1-uY/