Here is the full list of all 44 Nuclear Throne achievements. It takes around 200 hours to unlock all of the achievements on Windows.
Sit on the Nuclear Throne as headless Chicken.
Defeat Hyper Crystal.
Unlock a Golden Disc Gun or Golden Nuke Launcher.
Play as Frog.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Defeat the Technomancer as Steroids.
Reach 2-1 on Hard Mode as Chicken.
Defeat Hyper Crystal as Horror.
Defeat Captain as Rogue.
Unlock all Crowns as one character.
Loop as every character.
Reach 7-3 on a Daily.
Defeat Mom.
Reach Level Ultra as any character.
We hereby sincerely apologize.
Die.
Reach 2-1.
Reach 3-1.
Reach 3-?.
Reach 6-1.
Reach 5-1.
Reach 5-?.
Loop past the Nuclear Throne.
Defeat Horror.
Reach the Nuclear Throne.
Reach 4-? as Crystal.
Reach 2-? as Eyes.
Reach the Nuclear Throne in under 10 minutes as Plant.
Unlock a Golden Weapon for every character.
Eat a Hyper Weapon as Robot.
Defeat Mom as Rebel.
Unlock a Crown as any character.
Unlock a Golden Weapon as any character.
Defeat Big Bandit.
Defeat Big Dog.
Defeat Lil Hunter.
Defeat the Nuclear Throne.
Defeat Throne II.
Loop the game.
Reach Level Ultra as Skeleton.
Defeat the Technomancer.
Unlock Hard Mode.
Defeat Captain.
Get 100% of the unlocks.