Pretty simple. Get 300 multiplayer kills.
It may sound counter-intuitive but the best way to get kills quickly is to be a conservative player. Even the weaker guns can kill you quickly, and if you're running and gunning like a mad man through a level someone with a sniper rifle or an assault rifle will shoot and kill you quickly. The best to get kills is to find an accurate rifle with a scope. The sniper I've found best is the M107 and the Rifle is the EBR. Find a position that is hard to see that overlooks a lane of traffic and pick people off who are running and gunning. GRAW 2 is not a high kill game, so it'll take a little while. If you're an average player you can get about 3-7 kills a match.