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 as Rogue.
Loop as every character.
Defeat the Technomancer as Steroids.
Defeat Hyper Crystal as Horror.
Reach 2-1 on Hard Mode as Chicken.
Play as Frog.
Unlock Hard Mode.
Defeat Captain.
Defeat the Technomancer.
Defeat Hyper Crystal.
Defeat Mom as Rebel.
Defeat Mom.
Reach the Nuclear Throne with Melting without choosing Rhino Skin or Strong Spirit.
Sit on the Nuclear Throne as headless Chicken.
Reach 4-? as Crystal.
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.
Unlock a Crown as any character.
Loop the game.
Reach 7-3 on a Daily.
Reach the Nuclear Throne.
Defeat the Nuclear Throne.
Eat a Hyper Weapon as Robot.
Reach 6-1.
Reach 2-? as Eyes.
Reach 5-?.
Defeat Lil Hunter.
Unlock a Golden Weapon as any character.
Reach 3-?.
Defeat Horror.
We hereby sincerely apologize.
Reach 5-1.
Defeat Big Dog.
Reach 3-1.
Die.
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.