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