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Personally, I've seen that the demos for Stranger of Paradise: Final Fantasy Origin and Kingdom Hearts III omit trophy (achievement) lists. In the latter's case, I had to restart KH3 after I bought the main game to earn trophies that the demo left out. Right now, we don't really have a confirmed trophy list for Stranger of Paradise yet, but if there really is a "first level done" trophy, the demo will likely make players miss out on it.
Edit: Someone on PSNProfiles brought this up for Watch Dogs 2 here, and there's further info saying that achievements for Xbox demos would unlock for retail releases but not on PlayStation.
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