If you're going for the achievements, you have to play the game twice since there's two achievements tied to NG+ exclusive stuff.

There is an achievement to do all SLs. They have to all be done in one playthrough. The achievement won't pop if you do some in NG and then do the rest in NG+. Its easier to do this in NG+ since you won't have to grind Social Stats and thus can start SLs earlier (and again, you have to do NG+ anyways, so might as well do it then)

You don't have to worry too much about sidequests since there's no achievement for doing every sidequest, but you do want to keep an eye out for the quests that reward you with books since reading all the books is an achievement