In the St. Louis, Mo: Haven Level, there will be a small gun fight with a number of enemies. Then the game will take the camera and show a Brawler appearing and running through some cars. you need to kill that Brawler without taking damage.
This might sound hard, but it's rather easy. The first step to do is to use the Bullseye's secondary fire and tag a part of him, and shoot until it's dead as you back up. As long as you stay far away from the Brawler, he has almost no chance of hitting you.
Just keep up the attack. I was able to kill him just using Bullseye and Magnum. But I also had beaten the game and fully upgraded both weapons. If you don't get close to the Brawler though, you shouldn't have to worry about taking any damage.