I was thinking of doing my next playthrough to complete 100% of the game (I sort of rushed my first time), on the highest difficulty. Do I need to have multiple saves for branching scenarios, or is it actually possible to take a branch and then do some DnD shenanigans to get the results of all branches anyway?
You can do it on "one save", in the sense that you don't have to make another character. As Trappski had said, certain events/paths are mutually exclusive. You can play through the game on one path until you get all the achievements you can, and then load an older save.
This will let you do everything on one character, but I personally wouldn't say this is a "yes" answer to your question.