Not sure. I don't see why you'd need to have all the star coins, but it's possible that you'll have to unlock all the levels. They want you to be able to exit a level if you trap yourself, and you can only exit levels after you've already beaten them. I only have three-star files right now, so I can't really try it. I'm pretty sure you have to beat the game before it works, but I don't know about the other two stars.