Pauper
Survive day 30 by only gaining common items.

The most difficult achievement of the bunch, with Day 28 being particularly tough! Luckily, the spiral of death can solve most problems.

Recommended guild: Beekeepers

Basic strategy:

• Reset until you get Manure, you're going to need this to build your economy. Lock it so you can score it when necessary. Other buildables to chase are Dynamite (clearing obstacles), Garden Hose (enemy pathing), bamboo (damage buff). You will also want Chanterelle, the 3 Common Wolf items, and eventually Mead. Lock and obtain them when ready.
  
• Build a row of beehives between every 2 rows of Magic Beans. If you're worried about trampling, cap them off with a gnome or an extra beehive. You're targeting an economy of a few thousand gold per round. You'll likely have more money than you need by the end game.
  
• Late game, you're going to want to destroy your farms and build a spiral of doom.
  Build alternating Houses and Archers around a path of Swamp tiles. Surround the Archers with a layer of Bamboo for bonus damage.

Common items

• Lone Wolf items | +1 damage, +15% Crit Chance, -20% Cooldown when nearby no other Gnomes.
  Build Houses between your gnomes to use your space more efficiently. This achievement can take up most of the map and having to rebuild houses gets annoying.
  
• Chanterelle and Bamboo | Gnomes do +1 damage per nearby tree
  This item combined with Bamboo will drastically increase your DPS.
  
• Gold Top | Gnomes cost -1 Population, but get -100% XP
  Mostly useless with the Wolf items, you could build hedges instead of houses to save some gold, but money isn't the main issue in this run.
  
• Mead | +1 damage / -100% XP
  Likely will be essential in the late game. Buy it around Day 28.
  
• Crops | Coffee for Cooldown
  The main one that would benefit you in this strategy is Coffee, but its advantages seem limited compared to having Bamboo in the same tile.

Coffee or Bamboo?
My successful run I did it purely with Bamboo. And it's the simplest and most practical layout to build.

With 3 Bamboo, every base Gnome has 6 Attack, .6s Cooldown, and +20% Crit chance.
With Coffee, every base Gnome has 3 Attack, .4s Cooldown, and +20% Crit chance.
The ideal mix I've found is 2 Bamboo, and 1 Coffee, Due to similar damage output, but with the higher amount of attacks (120 vs 100 per minute) more attacks don't get blocked by the armored Goblins, which are typically the run ender on Day 28.

A few basic tests on a wave 30 map with level 1 gnomes gave me these results:
* 3 Coffee per Gnome was the weakest run.
* 2 Coffee, 1 Bamboo was about 20% more Damage dealt than 3 Coffee.
* 3 Bamboo was about 33% more Damage than 3 Coffee.
* 2 Bamboo, 1 Coffee was about 39% more Damage than 3 Coffee.

Due to the nature of the spiral, your gnomes might not always align, so full Bamboo is still the most consistent layout. Your mileage may vary here.

If you have leveled Gnomes, these differences should matter less, since a level 3 Gnome gets +2 Damage. This is more for situations where you're running out of space and want to get a tiny bit more DPS out of your gnomes.

Peasant
Survive day 30 by only gaining uncommon items.

I forgot to screenshot. This one should be flexible enough to do with a few strategies. I might redo this achievement to lock down a specific strategy.

Recommended guild: Townsfolk, Beekeepers require Fertile Soil management.

Basic strategies:

• Build a maze with your economy, Property Deed scales your damage nicely.
  
• If you want to use Beekeepers, goats are your best friend.
  
• Most specific gnome upgrade Relics (like Bodkin Arrows) are Uncommon items, use them.
  
• You can score Fleam (+30% Damage, -1HP/day) and Blood Whip (+1 Damage, - 1HP/day) during the final rounds for free bonus damage.

Prince
Survive day 30 by only gaining rare items.

Another relatively easy one. My run had 83 Archers and 420 Banishes.

Recommended guild: Townsfolk

Basic strategies:

• Reset until you obtain the Church, which generates a banish per nearby house per day.
  
• Play as you normally would, but build a Church in between each income generating set of taverns and houses, this will generate banishes which will be the backbone of your DPS.
  
• Keep building your economy and defences. You'll have enough banishes to get rid of all the Common, Uncommon, and useless items.
  
• You're primarily looking for the Monk Robes synergy, since it massively increases your damage by the difficult turns.
  
• Another beneficial item to get early is Ectoplasm, so you can create long lines of death with your archers. Your houses can route the enemies through your archers.
  
• Beyond that, just get what you want, you'll probably be okay.

Relic Hoarder
Survive day 30 by only gaining relics.

This one shouldn't be too hard. My run had a population of 376 due to the population increasing Morel which increases Damage per Mushroom.

Recommended guild: Townsfolk

Basic strategy:

• Build your economy with Taverns and Houses
  
• Clear obstacles with Jackhammer and get some bonus income from it.
  
• Get as many relic buffs on your Archers as possible.
  
• Score Ectoplasm to make killing lines with your archers, surround them with houses to funnel the Goblins.

Builder
Survive day 30 by only gaining buildable items.

I sadly forgot to screencap this run so I don't have the details right now, but it's mostly straightforward.

Recommended guild: Beekeepers

Basic strategy:

• Same broken economy as Pauper. Build rows of Beehives with 2 rows of crops in between.
  
• Statues increase Damage up to 2 tiles away.
  
• Wizards are great for AoE attacks, but they need to be a tile away from the path.
  
• Blunderbuss can stun at range.