When you start this level, you are playing with Buck, and you start with the Magnum and a Sniper Rifle. When you run into the first group of Brutes and Grunts, just take your time and take out the Grunts with the Magnum and the Brutes with the Sniper Rifle. There are plenty of walls, doors, and pillars to take cover behind. There is a turret on the far back left of the area near the door.
There will be several waves of them that come into the area from the door but enough will eventually come through that you'll easily get your 15 kills.
About 10 minutes is all it should take. The ammo you start with should be plenty.