What if, in addition to the rather basic "play 10 games" "win 3 games" "play 2/3 games with X herotype/franchise" we also had a separate system with varied rewards for pulling off certain activities in game?
Clutch heals, escaping near death, narrowly surviving fights you won in, saving a team mate, dodging skillshots, stealing a merc camp, assassination contracts on hero types or franchises, etc. Due to the variance it would be better to have a choice system where you select one of a random roll of three or so.
One of the major issues with this would ofcourse be people going out of their way to perform them or to force situations to get them, thus ignoring what is needed in the game and losing a match. Chasing the quest rather than playing the match.