Regarding the No Time to Waste achievement...
...you have to actually post a time to a leaderboard as it says, which means you have to be connected to Xbox LIVE for this to register. I got disconnected in a few levels but the achievement didn't unlock the way I was expecting it to (the game had registered a time for each level).
A time must be posted to a leaderboard, which you can easily check on the main menu to see the ones you may not have been entered into. The achievement unlocked successfully after posting a time in the level leaderboard I was missing.