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