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