I found this to be kind of a pain in the butt. For the record, it does not have to be 10 at a time, but rather just 10 over time. I tried over and over to get it so here is what I wound up doing:
Go into firefight, put it on normal, choose a mode, I chose the grunt one and picked corvette as the location. I then went into the game options, changed the Spartan health to invincible, the ammo to unlimited. I went into the loadout and made my loadout a needler so that I didn't have to bother picking one up. I went also went into the wave option, and changed the grunts to elites. The reason I changed to elites is I found it too easy to kill grunts with the needler without using the explosion.
Once into the game, pick an elite and shoot him with a burst that will just about kill him. If you shot enough needles, they will blow up and a pink star appears on the left of your screen for a few seconds. That star indicates that you got him with the explosion. Pick another elite and repeat, they don't even have to be close to each other. 10 of those stars show up over time, and the achievement pops.
I tried a few ways to get this on some endless grunt modes, and it didn't seem to pop even after scoring 50k or a million with a needler as my primary weapon.
Hope this helps clarify things for someone!