This will most likely be your last trophy, because the grind is real.
The best way to go about this is to immediately leave games. Even if you get 20 kills and win a game, the amount of extra Player XP you get is almost non-existent. It's not even worth wasting your time playing full games.
Begin searching for games (preferably solo lobbies so when you quit out, you aren't affecting other players) and as soon as you can pause, leave the game and immediately +queue up again.
This is incredibly boring, but it's the most efficient way of going about this.