Getting credit for this is slightly glitchy but the achievement should come over time from normal play.
I believe you can only get progress from normal missions (i.e. not bounty) and you may require a unspecified minimum amount of players to be in the match.
If you're boosting I would get at least three people and put two people on one team and those players will be the one going for the MVP medals, have the one person that's going for the MVP medal that mission do the objectives and get kills. Now repeat for the second player. Then for the third person you gotta switch up characters.
If you're playing solo against random players focus on kills first and once you know a objective is secure then go do it. Don't just focus on the objective as you might get killed and then the enemy or someone else on your team will get the objective anyway.