This is an easy one to figure out the achievements and to complete, but I decided to make one anyway just in case. It contains spoilers.
Hope it is useful.

IMPORTANT NOTE

This game has a point of no return. If you haven't completed the map and/or collected everything, do NOT interact with the cannon at the end of The Void. Regardless of the outcome of the fight you will be locked towards the ending and won't be able to return or even open the map menu.

Boss related achievements.

Abomination Killer - Defeat the Abomination
Pretty standard, just defeat the first boss located in the Excavation Site


Worm Killer - Defeat the Water Worm
This boss is located in the Drain Tanks after the submarine section.


Brains! - Defeat the Electric Brain
Boss in the Dome, after climbing the Command Tower


Spider Killer - Defeat the Carnivorous Spider
After killing the Brain, take down the lift on the left side to fight this boss and have access to the Black Market of the area.

Exterminator - Defeat the Hornet's Swarm MISSABLE
Missable. If you lose all the cannon HP on this fight you will fall into the pit and won't have a chance to get this achievement on the current playthrough.
Refer to "It's Not Over Yet" under Outpost 31 Section

Ace-est of 'em All - Take down the Centurion III
Final boss of the game, can't miss it.

A section covering progression/collectables related achievements throughout the game.

Ranger - Explore 100% of the Map
Just fill everything. The achievement should pop before reaching the end of The Void
Unfortunately I forgot to screenshot my full map before going past the point of no return. In the meanwhile, If you are also hunting for all specimens, the map on JCFrito's guide has all the secret rooms needed.

Heavy Infantry - Collect all special weapons
Just buy everything in the Black Market shops whenever you can.
They carry not only items needed for progression but upgrades for the units' arsenal and the nanotech injections too.

Bioengineering - Buy all nanotech injections
Same as above, just make sure to buy everything in the market whenever you can. Except for the ammo refill which is a consumable.

Parallel Universe - Find the secret room with Karak
Location marked on map on the Radio Outpost. Accessible through a breakable wall from the room on the left


Biologist/Mad Scientist - Find 15 Specimens/Find All Specimens
The number of specimens per area:
Intro - 1
Ventilation Tunnels - 2
Brood Chambers - 2
Extraction Site - 3
Nuclear Plant - 4
Command Tower and Dome - 6
Central Core (Mech segment when running from Laser) - 1
Drain Tanks - 5
Radio Outpost - 4
The Void - 2
For more detailed locations, check JCFrito's guide linked above.

Miscellaneous achievements

4 Colors' Enthusiast - Change the color palette at least once
Self explanatory


I Love the '90s Too - Use the color palette "Klendathu"
Also self-explanatory. Once you collect enough specimens you will unlock this homage palette to Verhoeven's Starship Troopers. Just select it once and the achievement will pop.

Worse Than Death - You turned into a mutant.
Fairly easy to get. On the Extraction Site there are creatures that resembles Facehuggers, just let one kill you and there will be a brief animation of your character turning into a Mutant.


It's Not Over Yet - Fall into the pit MISSABLE
The pit in question is the pit at the end of The Void after going through the door. Instead of defeating the Swarm, just let them drain the cannon's HP. You will fall into a pit with its own segment, reminiscing of Ropes 'n Roper.

Last Hope - Make Jade contact the Earth using the giant antenna in the radio outpost.
This is required for the good ending. Just select Jade and have her go to the Radio Outpost and interact with the console in the room marked in the map below.

Section detailing the endings

Purple Heart Hero - Finish the game with a good endingMISSABLE
For this one you need to have Jade contact Earth and to defeat the Hornet Swarm at the end of the Void. If your cannon HP depletes you will fall into the pit and will be locked out of it.

It's Just the Beginning - Finish the game with a bad ending
Just finish the game normally without having Jade contacting Earth, or if you did, just let the big hornets deplete the Cannon's HP so you fall into the pit.
It is actually a pretty cool ending if you ask me.

Arcade and challenge related achievements

Elite Soldier - Complete the training path in less than 30 seconds
This refers to the training area in the main game. It may take a few tries to get it and you have to wait for it to recharge, but it is pretty doable.
My suggestion is to use Tetsuo after you finish the game and unlock him, but your mileage may vary.

Cadet Sniper - Complete the shooting gallery once
Self explanatory. Under arcade, select Shooting Gallery and just finish it normally. It is quite long, but you can definitely get this along with Veteran Sniper on the first try.

Veteran Sniper - Complete the time shooting gallery with +2500 points
It is not difficult, just focus on accuracy over quantity.
Playing with Zeed through the game can help getting used to the mechanics of the Shooting Gallery

Runner - Complete the time attack mode once
Self explanatory. Just finish the course.
You can definitely achieve Raider on one try, but I'd suggest just running the time attack at leisure first to get used to the map and trap placements.

Raider - Complete the time attack without dying
Probably the most challenging achievement in the game.
While the Time Attack itself isn't difficult, traps will kill you. So try to get a good glance at the layout of the map and take it slow, there's no need to rush as there isn't any achievements for finishing the Time Attack under XX minutes.

At the moment this guide is considered to be a Work In Progress. There are a few things I want to add and complement, like more images and the maps, but the core of the guide is deemed completed so I am publishing it as is.
I hope it helps, and if there's something you want to see in the guide or have a question about, feel free to use the comment section.

Enjoy!