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