-Make an option to select a "low death run." it would take you to the world map and show all the levels as incomplete. When you beat them, they show up as cleared. And if you died, you would get one to the death counter. It'd make keeping track of levels you've beat in such runs easier. Sorry it's not the easiest thing to explain.
You could make it like Jumper 2, which kept track of how many times you've died in each level.
Not exactly my idea, but yeah an (optional) death counter would be pretty sick too.