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 Hyper Crystal as Horror.
Reach 2-1 on Hard Mode as Chicken.
Unlock Hard Mode.
Defeat the Technomancer.
Defeat Hyper Crystal.
Defeat Mom as Rebel.
Eat a Hyper Weapon as Robot.
Loop as every character.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Reach 4-? as Crystal.
Defeat Mom.
Reach the Nuclear Throne in under 10 minutes as Plant.
Unlock a Crown as any character.
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.
Reach the Nuclear Throne.
Defeat the Nuclear Throne.
Reach 2-? as Eyes.
Unlock a Golden Weapon as any character.
Defeat Horror.
Reach 5-?.
Reach 3-?.
Reach 6-1.
Defeat Lil Hunter.
Reach 5-1.
We hereby sincerely apologize.
Defeat Big Dog.
Reach 3-1.
Reach 2-1.
Defeat Big Bandit.
Die.
Defeat the Technomancer as Steroids.
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.
Defeat Captain.
Get 100% of the unlocks.