There is no easy way to boost for this so you just have to keep playing as best as you can to your ability. This achievement should unlock somewhere around once you are Level 28
-Use classes you are good at getting lot of kills with
-Stick with your team and follow orders from squad leader
-capture or defend objectives all the time (you get massive bonuses if you do)
-Play Conquest or Grand Operations in 32 v 32 lobbies as those 2 modes are most active ones in getting high scores
You should aim for averaging around 11,000-15,000 SCORE per game of conquest (~20 min/match) or around 27,000-30,000 SCORE in Grand Operations (~45 min/all 3 days of the operation)
Good luck and happy hunting!