Getting the kill isn't a big deal, but ammo isn't going to be as abundant as it is for other weapons. You cant just recklessly fire shots all over the place and hope to get a few kills. You need to make your way through an area as quick as possible and correctly aim at all the enemies that you see. You shouldn't have too much trouble getting this if you take car to shoot accurately and don't run out of ammo mid way through.
Defeat 10 enemies in 60 seconds with the China Lake Grenade Launcher