This is one of the most difficult challenges in the game. The reason it is difficult is that the point-of-view shifts, so as you walk through the streets you not only lose Krisis, but you lose the sense of where you are.
To beat this, I walked around the area and looked at how the camera shifted and figured out where everything was. Then I tried finding Krisis. You have to be pretty nippy with the keyboard in order to keep after him. It's one of those "lots of practice" things, unfortunately.
One other oddity: when you finally DO catch Krisis, you don't actually catch up with him. What happens is that the screen turns white for a moment, and then there's a cutscene in which you speak with him. There were a few times that the screen turned white, and I just assumed that I had died and went back to reload my game. If the screen turns white, don't do anything until you KNOW what's happening!