Here is the full list of all 44 Nuclear Throne achievements. It takes around 200 hours to unlock all of the achievements on Windows.
Unlock a Crown as any character.
Loop as every character.
We hereby sincerely apologize.
Reach 4-? as Crystal.
Reach 7-3 on a Daily.
Unlock a Golden Weapon for every character.
Reach the Nuclear Throne in under 10 minutes as Plant.
Defeat Mom.
Defeat Hyper Crystal.
Defeat the Technomancer.
Sit on the Nuclear Throne as headless Chicken.
Eat a Hyper Weapon as Robot.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Defeat Throne II.
Reach 2-? as Eyes.
Reach 5-?.
Reach the Nuclear Throne.
Loop past the Nuclear Throne.
Loop the game.
Reach Level Ultra as any character.
Defeat the Nuclear Throne.
Reach 6-1.
Defeat Lil Hunter.
Defeat Horror.
Unlock a Golden Weapon as any character.
Reach 3-?.
Reach 5-1.
Defeat Big Dog.
Reach 3-1.
Reach 2-1.
Defeat Big Bandit.
Die.
Defeat the Technomancer as Steroids.
Reach 2-1 on Hard Mode as Chicken.
Defeat Mom as Rebel.
Defeat Hyper Crystal as Horror.
Defeat Captain as Rogue.
Unlock a Golden Disc Gun or Golden Nuke Launcher.
Reach Level Ultra as Skeleton.
Play as Frog.
Unlock all Crowns as one character.
Unlock Hard Mode.
Defeat Captain.
Get 100% of the unlocks.