RUINER

You can do this on the easiest difficulty. In case you die, don't "respawn" - by restarting the game it'll load a previous save, therefore the death won't be counted. I don't think you necessarily need to restart the entire game and can just go back to the menu, but that's something you can easily confirm: the death count appears at the end of each level, so if it's zero - you're doing it right. The achievement will unlock after beating the game.