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