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