The best way to get this achievement is to do it while boosting the Team Battle achievements as it is the only game type where you have to shoot down opposing players.
In a standard boosting session for Team Battle everyone will be on Alpha Team except for one person who will be on Beta Team. Someone on Alpha Team will shoot down the Beta Team player so that Alpha wins. If your boosting for kills just keep killing the Beta player repeatedly.
Now if your the only player who is boosting kills then this is easy. Just let everyone know what you're doing and they'll usually just sit there while you rack up the kills.
If there are multiple people after this achievement then things become a little trickier as often people will fight for kills. If you can get everyone to take turns getting kills that solves the problem. If not, there is a way that almost guarentees multiple kills each game.
First off, select the F-22A as your plane and the XMA6 as your special weapon. This is the default setup so basically just don't mess with your plane settings. When the match starts everyone who is boosting kills will immediatly go rushing ahead to grab the first kill. Let them go and just stay at cruising speed. Once they get about a 10 second head start jump to max speed and chase after them. The planes in front of you will get the first kill and have to veer away to try and setup a shot for their next kill. When the Beta Team plane is destroyed it will leave a puff of black smoke in the air where it exploded. When you reach that puff of smoke switch to your special weapon and slow down to cruising speed. When the Beta plane spawns it will be right in front of you and most likely you will be the closest plane. Fire at least 3 of you XLA6s to ensure a kill (I always fire all six just in case some miss. It is also very unlikely that you will use up all of your missles over the course of the match).
Now to set up a routine to get you additional kills. As soon as you fire your XLA6s do a high G turn, speed up, and head back the way you came. Once the Beta player spawns again do a high G turn to line yourself up with their plane. If your quick you can get another kill right away but this is difficult and will probably annoy the other people playing so I wouldn't suggest it. Instead slow down and let the other players grab the kill. Again, this will leave a puff of smoke for you to aim for. This time though, you want to time it so that you reach the smoke right as the Beta player becomes available to target. Keep in mind that the Beta player can't be targeted for a couple of seconds after they spawn. If you time it right you will be so close to them when you open fire you'll be passing them right after you release your sixth missle. From this range it is almost impossible for anyone else to get the kill before you. If you keep repeating this pattern you can end up with half of all kills each session. For me that ended up being five or six kills every game.
A couple of final pointers:
1. Those black puffs of smoke that I keep mentioning. Use them not only as a marker for distance but also for altitude and direction. When a new plane spawns it will always be on a path that will lead them very close to that smoke.
2. Try and get a visual on your target plane while they still can't be targeted. When using the stratagy you will often be very close to the enemy plane when you can target them so if your trajectory is off even a little it can cause you miss when you open fire. The earlier you can spot them the easier it is to make corrections.
3. If for some reason things go wrong and you don't get the kill on your first flyby you still can get the kill. If you make a quick high G turn you should still be very close to the target plane. Just make sure that you have a good firing angle. Directly in front and behind are the best positions. It's amazing how many people I've seen who will unleash everything they have only to watch it all miss because they were coming in from the side.
4. If there are a lot of people after this achievement please be considerate and don't hog too many of the kills. You have to win 100 team battles to get all of the achievements so just getting two kills per game will net you your 200 kills.
5. Always, always, always save your game when you're done playing. The autosave function doesn't apply to online modes and with as long as these achievements take you don't want to be losing your progress because you forgot to save.