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.
Reach 2-1 on Hard Mode as Chicken.
Unlock Hard Mode.
Play as Frog.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Defeat Hyper Crystal as Horror.
Defeat the Technomancer.
Defeat Hyper Crystal.
Defeat Mom as Rebel.
Loop as every character.
Defeat Mom.
Reach the Nuclear Throne in under 10 minutes as Plant.
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 7-3 on a Daily.
Unlock a Crown as any character.
Reach the Nuclear Throne.
Defeat the Nuclear Throne.
Eat a Hyper Weapon as Robot.
Reach 5-?.
Reach 4-? as Crystal.
Defeat Horror.
Reach 6-1.
Reach 2-? as Eyes.
Defeat Lil Hunter.
Reach 5-1.
Unlock a Golden Weapon as any character.
Reach 3-?.
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.
Sit on the Nuclear Throne as headless Chicken.
Unlock all Crowns as one character.
Get 100% of the unlocks.