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