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