The game seemed interesting but I noticed there seems to be no back button. Is this his correct?

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I've completed the first and second worlds with three stars on each level, but it isn't giving me the achievements. Based on the completion bars, I think it isn't counting the levels I first completed in the demo. They were already marked finished the first time I loaded the full version, and I've replayed them in the full version, but I'm guessing the achievement can only detect the first time I completed it, and that happened in a version without achievements....