The key for this, and unfortunately it goes without saying, is balance.
How do you achieve a work/life balance when you're being forced to work virtually non stop? Well, for this I will refer to my university days where in the lead up to exams, it was pretty common to spend a month or so on a fairly similar schedule as yourself.
By and large, it should be fairly easy to stay physically healthy:
Avoid high sugar contents or excessive caffeine consumption. These are great for sprints where you have 4 hours to finish a job. But this isn't a sprint, this is a marathon. Binging on sugar and caffeine will help you on that day, but you will be in a real trough the following day and the day after (which will make you crave more sugar/caffeine and the cycle continues). I'm not saying don't have a coffee and a bowl of coco pops; I'm saying don't have four 500ml cans of Monster Energy.
I assume you'll be working at a desk as well so if you make sure you take regular stretches or short walks (even just to the canteen and back) every hour or so you should be fine. Otherwise, you will feel stiff and tired. Yoga or any other more intense exercise (a short run?) would also be excellent every few days if you find the time, but if not then don't worry too much about it.
Make sure you set up your desk properly: screen at the right level, seat adjusted, use the back rest, don't slouch etc. There is plenty of guidance online (first link on google I found: http://www.ergonomics.com.au/how-to-sit-at-a-computer/) on how to sit properly at a desk, but you need to be disciplined and actually follow it. You'll really struggle if two weeks in you find you've got a horrible knot in your back or twinge in your neck that makes using your computer uncomfortable. As someone who works a 9-5 office job, I can't really stress how big a difference this can make enough.
Also it goes without saying but try to get ~8 hours sleep a night. Don't stay up too late, with limited time you might really struggle to claw back a sleep deficit.
EDIT: Also drink water. Half the reasons people feel tired, depressed, lathargic etc is because they are dehydrated. If your pee is yellow and smells, you are already dehydrated and need to immediately drink water. If you are thirsty then it's already too late. Don't worry about going to the toilet every two hours, if your pee is clear and odorless then you are on the right track! Make sure you're always topped up. Keep a bottle on your desk, or leave a note to yourself.
Ultimately, keep your discipline, you're body should be totally fine. Don't stress too much about that. If you do all of the above, you'll probably end up healthier than you already are if you're of average fitness currently.
What you should be more concerned about is your mental health:
This WILL knock the absolute shit out of you mentally. You need to go into this with the right attitude and build yourself a few crutches to lean on along the way. Make sure you remember why you're there and how much this would mean to you to be accepted. Write yourself a little message on a post-it note and stick it to your desk, or bathroom mirror or at your bed to remind you that this isn't forever and that it will all be worth it in the end.
Work/Life balance is out the window, you don't have time to do the job and have planned time to yourself and sleep. What I would suggest is to make time for yourself, even 15 minutes every few hours: step away from your computer and go outside and get some sun. Don't even look at your phone. Just 'meditate' in the simplest form possible: do nothing. Do absolutely nothing and revel in it.
If the opportunity is there (which I imagine it is) make a few friends. Everyone will be suffering the same so see if you can build a few relationships with your peers. Also, you might start to feel homesick so plan for a daily phonecall to someone you know (even if it's just for 5 minutes) on the outside world (Partner, parent, friend) and let them know exactly how you feel.
Ultimately this entire exercise is about discipline: stay disciplined and focused on the goal, accept that it's going to be awful, and get on with it using every possible trick or crutch you have available to you.
And have fun too and best of luck. It probably won't be as bad as you expect!