Self explanatory really, get 50 double kills in one clip.
These are the maps that the Overkill is on (note that rotation means that this gun cycles between rounds with something else):
Old Town (rotation),
A couple of tips for the weapon, remember that the Overkill is a two burst shotgun. One when you press the trigger, and one when you release it.
The faster that happens, the bigger your spread. If the enemy is a little further away, holding your trigger and then releasing a little slower will allow you to get a tighter spread, and get more damage than you would if you released the trigger normally.
16 two shot bursts makes it a 8x2 kill potential if you kill enemies by gibbing at full health. I'm not sure for downed enemies, but for full health enemies a single burst (ie. pressing the trigger and holding it) will not kill, unless you have an active and aim for the head at point blank range.
I also link below a YouTube video by Tac-Com (full credit to them for some of the information in this guide), for those who like a little more information and explanation, and with more time.