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