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