For this Achievement you must kill the other teams flag carrier, while carrying their flag.*NOTE* This can be done many ways, this is just a way to make it a bit easier
My recommendation is to use one of the attack choppers (Viper or Havoc I believe they're called) You will want to be in the gunner seat
. Have your pilot (Helps if it's a friend) take you to grab their flag, I recommend while they have your flag. Grab their flag, and get back in the chopper, and have your pilot hunt down their carrier, and then all you have to do is kill him.*OTHER WAYS*
If you happen to have their flag on you, and you're at your own base, you can hide, and as soon as someone picks up your flag, you can attempt to kill them. You can also try the helicopter method with a tank, jeep, ATV, or any other vehicle you may find.
You can also just do it the old fashion way, and leg it, get their flag, and hunt down their flag carrier.
Hope this helped! Happy hunting!