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 as Rogue.
Defeat Captain.
Defeat the Technomancer as Steroids.
Reach the Nuclear Throne in under 10 minutes as Plant.
Reach 2-1 on Hard Mode as Chicken.
Unlock Hard Mode.
Defeat the Technomancer.
Defeat Hyper Crystal as Horror.
Play as Frog.
Defeat Hyper Crystal.
Eat a Hyper Weapon as Robot.
Sit on the Nuclear Throne as headless Chicken.
Loop as every character.
Defeat Mom as Rebel.
Defeat Mom.
Unlock a Golden Weapon for every character.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Reach 4-? as Crystal.
Unlock a Crown as any character.
Reach 7-3 on a Daily.
Reach 2-? as Eyes.
Reach the Nuclear Throne.
Reach 5-?.
We hereby sincerely apologize.
Reach Level Ultra as any character.
Loop past the Nuclear Throne.
Defeat Throne II.
Defeat Horror.
Reach 6-1.
Die.
Reach 5-1.
Unlock a Golden Weapon as any character.
Reach 3-?.
Reach 3-1.
Reach 2-1.
Loop the game.
Defeat the Nuclear Throne.
Defeat Lil Hunter.
Defeat Big Dog.
Defeat Big Bandit.
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.