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