I found that the Kill event called Friendly Fire is probably the best way to get this achievement. It is unlocked right after the mission you learn to fly a helicopter. In this event you fly an Apache and have unlimited ammo for all three weapons, and enemy helicopters are constantly coming after you in groups of 2 or 3. To get a gold medal in the mission you need 150 points and each helicopter you shoot down gives you 10. So if you can shoot down 20 you will have 200 points and will get the achievement as well as the gold medal. I completed this event on my 3rd try by flying around in circles backwards and constantly shooting my homing missiles and switching targets as soon as the one I was shooting at blew up. Keep a close eye on your radar to see what direction the next group of helicopters is coming from. Shouldn't be too hard or take more than a couple tries and since there is a time limit of 2:00 minutes it is really quick because instead of having to wait for more helicopters to (hopefully) spawn near you, they are guaranteed to spawn near you. Even if you don't get all 20 helicopter kills before the timer runs out, I'm sure that those kills will carry over into free roam (although I didn't test this) and then you can just find a couple more randomly flying around the city to kill. The remaining few you need should be easy kills since after the event your helicopter will have full ammo.