At the end of the mission "Assault Brayko's Mansion", you will have to fight Konstantin. The fight itself is simple, but you have to be on your toes the whole time. When the fight starts, do as much damage as you can to him right away, as the more you do to him now, the less time it will take to finish him later. After he's taken enough damage, he will stop for a second. Once the scene is finished, he will begin running at you with his knife. Shooting while running back is one of the few options you have, and when he gets too close, sprint away. Eventually, he will fall to his knees, during which he will be vulnerable.
If you don't kill him by this point, a bright light will flash, and he will have his SMG's again. Also, several of his men will come in, so take them out right away. At this point, the pattern will keep repeating itself until you finally take Brayko down, so keep at it.
Once taken down, you'll finally get the chance to speak with him. Just make sure at the end of all it all, you spare him.