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