Here is the full list of all 44 Nuclear Throne achievements. It takes around 200 hours to unlock all of the achievements on Windows.
Sit on the Nuclear Throne as headless Chicken.
Unlock a Golden Weapon for every character.
Loop as every character.
Defeat Captain as Rogue.
Eat a Hyper Weapon as Robot.
Defeat Captain.
Reach 7-3 on a Daily.
Defeat Hyper Crystal as Horror.
Reach 2-1 on Hard Mode as Chicken.
Defeat the Technomancer as Steroids.
Reach the Nuclear Throne in under 10 minutes as Plant.
Defeat Horror.
Play as Frog.
Reach 5-?.
Defeat Mom as Rebel.
Reach 4-? as Crystal.
Unlock Hard Mode.
Defeat the Technomancer.
Defeat Hyper Crystal.
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.
Reach the Nuclear Throne.
Unlock a Crown as any character.
Defeat the Nuclear Throne.
Reach 6-1.
Defeat Lil Hunter.
Reach 2-? as Eyes.
Unlock a Golden Weapon as any character.
Reach 3-?.
Reach 5-1.
Defeat Big Dog.
Reach 3-1.
We hereby sincerely apologize.
Reach 2-1.
Defeat Big Bandit.
Die.
Unlock a Golden Disc Gun or Golden Nuke Launcher.
Reach Level Ultra as Skeleton.
Unlock all Crowns as one character.
Get 100% of the unlocks.