Note: Disable Helicopter is handy in this mission if you want to get the helicopter off your tail, so purchase it if you haven't.
When it becomes clear that you're not gonna give Damien what he wants, he plasters your image all over the town.
Head down the stairs and make your way across the street, with the news van nearby. I find that the best thing to do is to reload until a motorcycle is between you and the van, as it has the speed and the control you'll need. With the motorcycle you should be able to take out the broadcast van quickly with the first Traffic Light and finish the driver off with your gun.
If you miss out on taking out the van on the first light you will have to deal with the police scans while trying to finish off the driver, which makes the tasks of quickly and easily finishing an issue. If this happens, I suggest you simply reload the checkpoint.
No matter what you do, you can't outrun the scans forever, as they will continue to scan you until they track you down through multiple districts. The best thing to do is to rush for Pawnee and use the backroads to lose the police cars and disable the helicopter and get away pretty easily.