Rather than go for the 10 kills at the beginning of the level with the hoard that comes, conserve your ammo, there are 5 wraiths you can kill netting you a total of 15 kills.
Look all the way across the bridge and you should see 3 wraiths. Kill those wraiths and it will get you 9 kills. Then keep the rest of the ammo and take care of the hoard whichever way you want. (excluding the laser)
EDIT: If you're looking for a quick way than you could just take a shot at any enemy at this point and it should only take a minute or two. If you're actually playing through the level I suggest conserving the ammo for the other wraiths.
When you pass through the gate there will be phantoms dropping off reinforcements, they will drop a wraith on both sides of this part of the level. Once you kill the 4th wraith you will get the achievement, and the 5th will give you 15 kills.
There will be one more wraith dropped in the middle, but you should be out of splaser ammo now, so you can kill it using whatever other method you may like.
By only killing these 5 wraiths you will easily get 15 kills and another achievement to boost your gamerscore.
Note: This was done on Normal and Easy difficulty.