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