You will need to unlock and equip the Czerka (Republic) or Sienar (Empire) Seeker Mines with a component point. The X-Wing and the TIE/LN are the only ships that can't use them.
I got this is Fleet Battles vs. AI. I chose an A-Wing for its maneuverability and speed, but use what you feel most comfortable with. My only goal for the match was to fly around to where enemies clustered and drop the mines. I had equal success damaging enemies (the mine will blink yellow or red when it has a target) during the offense and defense segments, and popped the achievement 3/4ths of the way through the match on my first try.