Here's the deal:
I had the same problem with this mission; which is crazy, since it's like one of the first ones you do!
The secret is to stay in a car for as long as possible. You can shoot your gun while sitting in (relative) safety from the car. The other point to make (thanks @spartacus) is only killing the marked gang members. Once you wipe out the marked members, drive to the next area and again remain in the safety of your car. The car you start out with will have a very high tolerance to damage, and if it happens to light on fire, get out and steal a new car! As an added precaution, try to park your car in such a way to block the sight lines of the snipers. This is hard, but the first area allows you to park the car in the little alley and shoot the gang members, and will prevent those darn snipers from drawing a bead on you for a little while.