For this achievement the game will recognize the exact date AND time of a full moon for the unlocking requirements. Instead of marking your calendars or getting up in the middle of the night, you can change the clock settings on your actual phone. Go to Settings>Date and Time, set clock to manual and change it to May 17th, 2011 at 5:07 AM (the full moon occurs during the 5:08 minute, but this gives you time to enter a game quickly. There is some leeway for this but might as well get it as close as possible).
Now enter a game and float for 2-3 minutes, then spend all your fuel up. The achievement should unlock at the end of the play session.
If you want to do this achievement the way it was intended, here is a calendar of all the full moons for a number of upcoming months/years: