This achievement is a lot easier than it sounds. Instead of finishing the entire game on the hard difficulty which sounds daunting, you can simply finish the final boss on hard.
If the final boss is too much of a challenge for you, grab a spare controller and set it on easy. Once you enter, quit with the spare controller and restart the level. Fight the boss with the spare controller until his health is pretty low and then – when on the verge of death – sign in with the controller you want to get the achievement with and defeat the boss. You’ll need to die with the spare controller before you defeat the final boss or it will register him as being easy.