To get this achievement you will need the fallen ghosts DLC. The next thing you want to do is complete the first mission (this is were you will find your first cross bow), after you grab the cross bow, you should open you menu and spend 1 skill point in explosive bolt. Now all you need is a helicopter to shoot down!
For this you can do one of three things, 1 play the game till you find a helicopter, 2 play a defend the radio tower (green mission), or 3 have a friend fly a helicopter around till you see an enemy helicopter, then shoot it down. Remember if you EMP the helicopter, and it's on the ground this will not work. This video will show you how to unlock the achievement.