This is story related and cannot be missed.
This achievement is available to acquire in the final mission, mission 20.
At the very end of the mission you will be challenged to a one-on-one dogfight against the person you need to complete your revenge. This fight is the hardest out of the lot of them due to one reason; he will stick to your back as hard as he can. You will have to outmanoeuvre him to get your shots on. Providing you can stick behind him even if you are not getting many shots off, it means he cannot hit you. So just keep hitting those few shots at a time until he is down.
The two tactics for these are to either follow the pilot until he goes outward to try to get on your six, or you could fly out yourself and hopefully will not get followed so when you turn around you can cause some real damage.
The achievement will unlock once the enemy Ace is down.