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