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