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