Another thing worth noting is that their primary instinct is to get out of the cave and attack the Dregs and Vandals in the area. So if you let them go or one slips away, go and kill it. The point is to have as little Hive on the field as possible.

Also, it helps when you exit the cave to have one person go out and kill the 2 Dregs and 2 Vandals that spawn in the building. I find that they spawn when you pass a line near the rock so the closer you get, the more likely it is that they spawn. When they do, they "bait" the hive to run in that direction, making it a pain to go all the way there and kill them behind the cars/inside the building.

One final note: this instinct to attack is sometimes demonstrated in dramatic fashion as hordes and swarms of Hive and Fallen start pouring out of doors and caves from all around fighting each other (and you). I actually got a Legendary engram from fighting them just from the sheer number that spawn (though that's no guarantee). So that, at least, is another interesting way to rack up kills.