To be MVP, you have to reach a certain amount of objective points in whatever gametype. They are as follows:
TIES WITH ANOTHER PLAYER FOR MVP: There are no co-mvps. If you are tied with another player it seems the selection is random.
IF IT IS A TEAM GAME you need to lead the game in scoring, not just your team.
King of the Hill: Have the most hill points
Team Slayer: Have the most kills in the game. If you are tied with someone else, it seems like it is just a random selection.
Oddball: Have the most time with the oddball in your hands.
CTF: Score the most flags in the game.
VIP: Kill the most VIPs in the game
Territories: have the most territories captured
Infection: This is sorta FFA, but you need to have the most points from killing infected and infecting by the end of the game.
Juggernaut: Kill the most people in the game as the Juggernaut. Once again this is also sort of a FFA.
Bomb: Score the bomb the most.
This covers every gametype, hope it helps! My first shot at a solution!
EDIT: I HAVE BEEN INFORMED THIS IS NOT AVAILABLE IN FFA GAMETYPES!