In Dogfight mode the target is to kill your opponent to get enough points to win the game by score or before the time runs out.
This can be boosted by setting the Score to 5, Scoring System to Kills/Suicides and either have the one person kill once and then fly around until the time runs out. Or one person can just fly into the floor and his/her score will turn into a minus. 0 being higher than any negative number means victory.
The achievement will unlock at the end of the match before returning to the lobby.