I remember at one time viewing an episode of Xbox 101 and it indicating that you can delete acheivements if they are at zero. I don't see any old episodes of Xbox 101 on Xbox Live. Would anyone know how to do this?
Center button on the controller. Left to achievements, go to the game with 0 points and you should have the option to push (X) and "Delete Game History".
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Yes what Raok said. Remember you can only delete games that you have not earned a single achievement for.
and to add if you ever get your score reset for cheating all the zero scores that are there from the reset cannot be removed, just throwing it out there ;).