Bit of important information:
- it is _not_ possible to do a single run and get all the achievements without explicit use of save games. Keep this in mind during your playthrough and save at critical points.
- there are multiple achievements based on decision points that sometimes require choosing 3 different possibilities (e.g. Aspen) or play through whole chunk of story with two conflicting approaches (e.g. Holy Detonation DLC). Whenever there is an important decision to make, create a separate save game for it. Best to also do that for every new location you enter.
- this will not be an achievement collection guide, there's already plenty of those - I personally found the one here to be quite useful to work with, though it doesn't have any spoiler alerts so be careful. This is going to be a 'where to be careful not to mess up your trophy run and have to play the game again' kind of a guide.
- having above points in mind, I will not be including here all the things that can be done within 20 minutes from a random save game, but rather achievements that, if approach incorrectly, will require you to go back hours of gameplay.
- there's quite a lot of those listed below and this list only means that if you follow it, you will not mess your save game in a way that will prevent you from getting any of these achievements. You may still need additional work to get some of these achievements and others.

@EDIT 4th Feb 2023:
New content in italics. Due to the lack of time I could not investigate those mechanics in the game.
Thanks to Squall and Icedfate for providing their feedback!

1. The Scientist
Pizepi Joren has offered to join your party.
Do NOT kill The Gift in Aspen or you may block this achivement.
2. Body Builder
Get modded, and be able to install cyborg parts.
You will not be able to obtain this if you work with Wolfe and kill the synths. If you try to do this and later work with Wolfe, you will not get the Combat Shooting book. Best to just make a save game when meeting Vivisecto, buy & install the mod, then reload.
3. Back in the Sack
You collected all STDs in the Wasteland.
Missable if you kill Brygo (which you probably should anyway). Best to do this as soon as you get access to Little Vegas (most of it anyway, one last part will require more hassle or just moving with the story).
4. Bawk
You assembled Poultron.
Once you come across any of the robotic chickens, if you decide to tame them, make sure to visit Animal Kennel/Chicken Coup at Ranger HQ ASAP. They are know for disappearing and are not that hard to accidentally kill in combat and you need 5 of those for the trophy - just as many there is in the world.
5. Double the Fun
Bring Billy and Jean all the way to the end of the game.
Missable if you choose to save Arapaho Caravan instead of Hoon Homestead. From story/achivement perspective, best to save the homestead (also matches with another achivement). Oh, and don't tame the goat until the end game, unless you want to be super careful to not get it killed.
6. Toaster Expert
Earn your toaster repair diploma.
Do not sell any of the golden toaster parts.
7. I, Human
You convinced the Machine Commune that humans can be trusted.
There's a couple of actions that will be viewed as negative by the machine commune. Best to read up on it before interacting with anyone in there. Also, do not hunt more synths than the first one, otherwise this might mess it up for you.
8. Illuminati
Uncover the darkest of conspiracies.
You need to bring Provost with you to Snowed Inn Resort and fix a toaster there, which will open another location on the map. Best to grab Provost right before going to SIR.
9. Restraint
Resist temptation and never open the Mysterious Case.
As above, you'll get your reward at some point and it will be worth it.
!!! 10. Tricked Out !!!
Obtain all vehicle upgrades.
Nitro-Ray can be missed - you need to kill Wind-That-Tangles in "Disappeared" quest.
Electronic countermeasures can be missed - if the player chooses any outcome that loses rep with the gippers before finding the random encounter outside.[/i]
Railgun can be missed - if you don't bring Valor back.[/i]
11. Menagerie
Tame at least one of every type of animal companion.
Make sure to grab Major Tomcat in the very beginning, Billy and Jean (allegedly, didn't test it) later and bison from Knox Bison Ranch by helping the farmers. Rest of the animals cannot be missed as long as you don't kill them.
It seems that you need Animal Whisper 9 before "helping". Also other sources says that you need to talk to Knox's in the chapel (in the city) before you start the quest.
I can't confirm or deny which of the two is needed, because I failed in both, but for sure I missed a bison and thus the achievement :(
12. Answering Machine
Find all the cassette tapes left around Colorado.ri
You can miss a tape from Hoon Homestead if you don't save them from Brygo if you don't kill him. As of v1.6.9.420, I was able to get the tape off Brygo even though I sided with him before (he was still in Little Vegas), but it's better to kill him anyway.
13. Book Learnin'
You found every lore book in the game.
There are 3 books/notes that can be missed/lost. How to avoid that:
1. Search all corpses in Ranger HQ medbay the first time you're there.
2. Do not give Old Journal to Miriam Knox (untested, better safe than sorry).
3. When Patriarch offers you a prisoner the first time you talk to him in RHQ, you need 2 leadership or more for a skill check - use that option, then get to Magistrate Silas and ask him about the prisoner.
14. November Reigns
Team November and the Rangers have taken over Colorado.
There is a couple of story choices you need to take to make this possible:
1. Gippers have to continue delivering Oil to Colorado Springs.
2. Loved rep with the Marshalls - that's why you should kill Brygo.
3. Loved rep with the Hundred Families.
4. Have Gideon Reyes at your HQ.
15. All in the Family
You listened to all of Archie and Edith's shows.
Best to do it straight away after getting to Steeltown, as with everything that happens later they might be dead.
16. Oh Hey, Bros
You found the strange mushroom shack.
For this one, you need to release the strange prisoner from the jail cells in Ranger HQ in the beginning of the game.
17. Ryan Shame
You wiped out the Ryan family line.
Depending on your choices, best to do this before you pick a side in Steeltown.
18. You Had One Job
You tricked Keith into getting roasted by the fire jets. Self explanatory.
19. Clone 2: Genetic Boogaloo
Created an Uber Clone or the Flesh Prince using Irv's Cloner.
Be careful when you get to the cloning equipment in Holy Detonation DLC, because if you purge the stuff from it, you might not be able to get this achievement.
20. Flawless Espionage
Managed to unlock Bezoar's laser wall without being detected.
21. Like, Totally Shroomin' Out, Man
Consumed every type of irradiated mushroom.
Best to pay attention and not waste mushrooms from the Research Level of Cheyenne Mountain.
22. Super Secret Sabotage Sauce
Made 1000 Island Dressing and used it to sabotage the Particle Accelerator.
There are 2 recipies that use the same ingredients. If you make the sauces wrong - you will miss the achievement.
23. Kumbaya
Re-united the Nucleists and Primordialists.
The only way to unite Nucleists and Primordialists but requires a sacrifice of one of your rangers - best to create a fresh one and bring them just for talking to Deuterium, after giving it 10 holy radiation.
Requires Father Bezoar to be rescued and alive - not possible to complete if he's killed or transformed.

1. The Needs of the Many / Hoon Hero / No Time for Distractions
Once you get called to pick Caravan or the Homestead, save the game for later replay as this has 3 achievements related to it.
2. Stolen Valor / Valor's End / Won One for the Gipper
Three outcomes of one decision, make a save before deciding the fate of Valor.
3. Caged Psycho / Victory Over Victory / The Psychopath
Same as point 2 but for Victory.
4. Give Me Liberty, Or... / Un-Lib-erated
Same as point 2 & 3 but for Liberty.
5. Companion achievements (The Marshal / The Gunslinger / The Warlord / The Hard-Head / The Psychopath / The Hobo)
Not necessarily missable, just make sure to have a save before first encounters with Darius Kwon, Lucia Wesson, Ironclad Cordite, Fish-Lips & Victory Buchanan in case the convo would go sideways. Pizepi Joren is in the missable section.
6. Morningstar / Bunker Buster
Two outcomes for Morningstar.
7. Blue's Back / CEO / Workers United & Perfect Pacifist / Killing Machine
You will need two full runs of Steeltown - one without killing Ghosts or workers through using disrupting weapons (allegedly, this also goes for initial fight with the Ghosts - for that fight either non-ranger AI finish them or hit them with aimed shots for their spinal implant, which will shut them down) and one while killing _everyone_ you fight with (so no spinal implants to be safe).
First run is best for Blue's Back achievement (be careful and don't use Hard Ass against his gang), second can get you to the point where you have to pick sides between Crow and Markham, from which you can get both achievements after just few fights.
8. No Bezoar Left Behind / Necessary Evil
Two options for Father Bezoar.
9. Lightning In a Bottle / God Killer
Two options for Holy Detonation. Third option isn't really an option, it ends the game and gives no achivement.
10. Dead Red / New Colorado Order
Save your game before leaving Yuma after defeating Liberty - two options to choose there.