Here is the full list of all 44 Nuclear Throne achievements. It takes around 200 hours to unlock all of the achievements on Windows.
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.
Defeat Hyper Crystal as Horror.
Defeat Hyper Crystal.
Defeat Mom as Rebel.
Loop as every character.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Reach the Nuclear Throne in under 10 minutes as Plant.
Defeat Mom.
Unlock a Crown as any character.
Unlock a Golden Weapon for every character.
Reach 7-3 on a Daily.
Loop past the Nuclear Throne.
Defeat Throne II.
Loop the game.
Reach Level Ultra as any character.
Eat a Hyper Weapon as Robot.
Reach 4-? as Crystal.
Reach the Nuclear Throne.
Defeat the Nuclear Throne.
Reach 5-?.
Reach 2-? as Eyes.
We hereby sincerely apologize.
Defeat Horror.
Reach 6-1.
Defeat Lil Hunter.
Reach 5-1.
Unlock a Golden Weapon as any character.
Reach 3-?.
Defeat Big Dog.
Reach 3-1.
Die.
Reach 2-1.
Defeat Big Bandit.
Unlock a Golden Disc Gun or Golden Nuke Launcher.
Reach Level Ultra as Skeleton.
Play as Frog.
Unlock all Crowns as one character.
Get 100% of the unlocks.