Spawn at a point which is located near many enemies (gang memebers). It's best if it the location is close to a gang leader as their locations are usually crawling with gang members. I find this achievement easiest if you use the missle launchers. Select the "Hothead" and the "Firefly" as your primary and secondary weapon. They both have long range and deal a great amount of explosive damage.
Now use your missle launchers from a distance and pick off groups of enemies. Once you are low on ammo, return to the spawn point to reload, then back to your gang leader location to pick off more enemies with your missle launchers. Repeat and have fun.
Be sure to be careful with your aim and try to not hit any civilians as it will alert the agency.
This will give you good experience to build on your Explosive rating and also earn the Explosives Expert achievement.