Simply consume all different types of food, including drinks, to gain this achievement.
As all other multi-playthrough achievements, there have been reports of it not unlocking when it should. Try to contain the requirements in one playthrough, to be on the safe side.
A walkthrough can be found here.
Note: All types of rotten food can be found in trash cans INSIDE the restaurants of the Food Court. Do not bother with the ones outside, they often only have sodas/guns/snacks. You only need to eat one rotten food, not every one of them