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 4-? as Crystal.
Defeat the Technomancer.
Reach the Nuclear Throne.
Unlock a Golden Weapon for every character.
We hereby sincerely apologize.
Reach 5-?.
Reach 7-3 on a Daily.
Defeat Hyper Crystal.
Defeat Mom.
Reach Level Ultra as any character.
Reach 2-? as Eyes.
Defeat Horror.
Loop past the Nuclear Throne.
Defeat Throne II.
Unlock a Crown as any character.
Loop the game.
Defeat the Nuclear Throne.
Reach 6-1.
Defeat Lil Hunter.
Reach 5-1.
Defeat Big Dog.
Die.
Unlock a Golden Weapon as any character.
Reach 3-?.
Reach 3-1.
Reach 2-1.
Defeat Big Bandit.
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 the Technomancer as Steroids.
Eat a Hyper Weapon as Robot.
Reach 2-1 on Hard Mode as Chicken.
Defeat Mom as Rebel.
Defeat Hyper Crystal as Horror.
Defeat Captain as Rogue.
Unlock a Golden Disc Gun or Golden Nuke Launcher.
Reach Level Ultra as Skeleton.
Play as Frog.
Sit on the Nuclear Throne as headless Chicken.
Unlock all Crowns as one character.
Unlock Hard Mode.
Defeat Captain.
Get 100% of the unlocks.