This is fairly straight forward, but I want to mention that "maximum reputation" means that the faction has "revering" next to your name. You do not
need 100% rep for this to unlock, unlike what some guides like Powerpyx are saying.
Personally, I got it with Deserters, Spacer's Choice and Groundbreaker. Spacer's Choice is at 100%, Deserters is at 78% and Groundbreaker is at 78%.
So if you're stressing a bit, just do all the quests for a faction and you should get it without an issue.