First, go to a boat shop or hangar (green icon on map) and get a sea plane with a machine gun (Carmina, Clusterduck, The Wild Goose). The Carmina plane is unlocked automatically from the "Air Raid" story mission in John's region (Nick is the mission giver for it). Then, spawn another plane and use the machine gun to destroy it with your plane. Stay parked on the ground while doing this, as there is no need to fly. After destroying the plane, spawn a new one and repeat the process until you get the "Ace Killer" achievement.