I was wondering if it is possible to segment the all achievements run as I am unfortunately busy with university and cannot play more than three hours at a time but really want to try it. My plan is to play a few hours every weekend but I was wondering if that would still be considered a legit run? Do I have to do it all in one go?

You have to do it in one go

All advancements doesn't have to be done in one sitting, as long as you show yourself opening and closing the world in the video you'll be fine