I would still want to keep badges per character, but I think it would be cool to see kind of an "Account Progress" tracker that applies to a persons overall account. In my mind it would include overall badge progress against all badges capable of being obtained. The idea kind of stems from Guild Wars 2 and their map completion, but there's is typically character based. I know there are Hero and Villian separate badges, if there is a badge that is the same for both Hero and Villian count that as only needing one, but badges that are specifically for a Hero or a Villian like Task Force badges, those should be separate.
Once you reach certain milestones, every 10%, 20%, or 25% give a reward of some kind.