Loosely follow "DrNewcenstein's Non-Confrontational 5 & 7 Day Survivor Guide for Dead Rising" which can be found herehttp://dr.newcenstein.com/non-confrontational.html
That guide will enable you to get all of the static food with minimal confrontations.
Use Hoddans Survival tool, which can be found herehttp://hoddans.com/tool/drsurvival/
Use it to check off the food as you collect it, and keep easy track of the in game time (you don't have a watch in infinity mode). By selecting food from the drop down box, you can see how many health blocks you will gain from consuming it (remember to to put a tick next to the health books you collected).
Additionally, you can see which psychopaths and survivors are active in what location at what time and tweak the Non-Confrontational guide accordingly. The psychopaths in particular give out huge amounts of food, so even if you take a beating from them, the reward should far outweigh it.
Lastly, use the dead rising alarm timer by dyxtra, which can be found herehttp://www.dyxtra.com/deadrising/
I would advise setting a conservative time to ensure you have the food ready and dont die a silly death. You could also use a wireless controller, which should switch off with plenty of time to spare, BUT ONLY IF you are at full health when you put the controller down!
This achievement will take 10 hours of real time to obtain, there is no way to save, but you can pause.
Needless to say, once you have invested ten hours to get this achievement, you might as well carry on a little longer and get the achievement for surviving seven days.