Grand Theft Auto IV/United Liberty Paper

This is a challenging chase mission, although the only way to lose it is to spin out or crash, and cars will constantly be pulling into or in front of you. No matter how fast a car you have, he can drive faster, and if you have a slow car, he will wait for you. Since speed isn't a factor and surviving crashes is, the best car to use is the Hummer clone, which lets you go right through crashes. Just slow down for turns and you should be able to keep up.

He goes down some narrow alleys, but you can avoid them by going to the next parallel street. Just watch the HUD to see where he is going. If he gets on a bridge and you miss the turn, you are done.

After following him for a long while, he will start letting you get closer and if no cop cars are around, you should probably take a few shots and/or bump him. You may also get a chance to box him in by getting on his left when he is behind a slow car.

Eventually he will stop and you will get a message to finish him off. Get out of your vehicle and do so.

Portrait Of A Killer
You will not come away with the car you drive to ULP, so don't take one of your favorites. If you have full health and armor, you shouldn't use more than a quarter of it.

You start by having to boost a cop car, searching for a Bad Guy ("BG"), and going to where he is located. Cop cars are great. Turn on the siren and everyone gets out of your way; you don't have to stop at toll booths; and they are very fast and take a lot of abuse. So when the mission is done, you may want to keep the cop car.

The guy you are looking for has an army of BGs around him. From behind a telephone pole at the building across the street, you can snipe a lot of them without taking much damage. (It would be nice if you could get on top of that building, but you can't.) When no more are visible, switch to your weapon of choice and cross the street to finish them/him off. Just look for the red dots on your HUD.