The easiest way to get this achievement is to first complete driving school. There are 12 tests (some of them are a little challenging) and once you complete them all with at least a 70% or above you will complete driving school. After you exit you will receive a call from Jethro and at that point you will unlock all the illegal street races around the map.
The race you want is the one inside the Las Venturas airport just inside the gate which are all air races. When you stand in the red circle you want to select Heli Hell as the race. When the race starts you will be flying a Hunter (Apache). At this point ignore the red circles/coronas. Exit the vehicle and wait for the timer to run out. Once it is over you will "fail" the race and exit. However the Hunter will still be where you parked it.
Get in and click
to start the vigilante missions (FYI they are called Brown Thunder in the helicopter but it doesn't matter.) Now fly to the targets and kill. Once you are in range hit
for machine gun which auto targets the enemies. You can also use
for rockets but they do not auto target. Just be careful not to crash or blow yourself up and you should have plenty of time after the first 1 or 2 targets.