The Full Moon Egg was one of the eggs found in the Egg Hunt 2013.
This egg was easily obtainable like other eggs, with a catch. It could only be found at night, which means you would have to wait every time you missed it.
Although this egg is easy to get, if you do not happen to find it, you will have to wait a full day in-game to get another chance. This made it moderately hard to obtain.