Minecraft: Xbox 360 Edition

Starvation is when your hunger bar runs out and you start losing hearts from your health bar. This can be achieved on any difficulty except peaceful. Make sure you have Rotten Flesh from a zombie and you are in a safe place. Sprint and jump until your hunger is gone and you start taking damage, then eat the Flesh. (It takes about 3 minutes for the hunger bar to deplete from full on any difficulty.)

Since the new update, this has gotten a lot harder, because they've now fixed the hunger systems so that hunger doesn't degrade so fast. I couldn't manage to get my hunger to drop enough with normal play, I'd always end up dying before my hunger dropped.
The solution for this is as follows, first off kill a zombie to get some rotten flesh (difficulty easy or harder) load up the game on the hardest difficulty (hard), and go inside to somewhere relatively safe. Now keep jumping until your hunger drops. It will take quite a long time, more than twenty minutes. Once you go into starvation, eat your rotten flesh and the achievement will unlock

The two methods above can be combined to save time. Sprint until your hunger bar has depleted seven of the ten food indicators, ensure you're in hard mode, and jump in place to deplete the other three. This process took me roughly five or six minutes.