Try memorizing all the letters that the country begins with to start off with as this will be a great help so you'll at least have a chance at remembering if you forget. Then memorize them. Read over the first one three times, then second, then third, then all the way up to 50 or so for the first day. Then do 50 more the next, and 50 more the day after and so forth until you've gotten them all, so 4 days. Then on the final night spend a little more time going through them all a couple times, but by now it should be much easier. This is just what I would do if I had a big memorization test like this. Good luck.
Edit: Didn't know you had to label them on a map. Do what I told you to memorize the countries, then additionally practice labeling those 50 countries you memorize on the map each night too.