This achievement is gained once you have stopped starving by consuming rotten flesh. This must be done on survival. You cannot do this on peaceful.
For this you will need rotten flesh.
Rotten flesh is a common drop from zombies. These monsters appear on the surface at night and spawn in dark areas regardless of the time.
Your hunger bar is the bar on the right and looks like a string of meat.
As it depletes the bar will gray out. Once it is fully grayed out you will begin to starve, and take damage regularly. It is during this time that you should eat a rotten flesh. This will ungray some of your hunger bar and the achievement should unlock.