One major point that I'd like to make clear for everyone is that your vehicle can count as one of the three vehicles. I connected a second controller and was playing against a friend. We ganged up on one vehicle to the point that they had low health and then I finished the the AI and his vehicle off. Within a few seconds of staying still my vehicle exploded and the achievement popped. This might be more of a tip than a solution but just understand that your vehicle can count as one of the three.