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