Wrong Is Right
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.
This is a good opportunity to use the cop car you just saved. You are going to have to follow a helicopter, and your sirens blaring will make it easier. The helicopter will veer off the main road, but you can just stay on it, even to the point of taking the tunnel and losing sight of the chopper for a few minutes.
Eventually you will turn left towards where the chopper is landing. You should get a prompt telling you to wait for it to land. Two BGs will try to stop you. You can ram one, but the other one will shoot you, so just stop short of them, get out and shoot them, then get back in the car and drive down the path. You can run into a group of BGs, but it doesn't seem to hurt them and you will catch a lot of damage trying to back up.
A better idea may be to quickly drive to one side of the building or the other so that you can get out and take cover, then take your time knocking them off.
Since this is Introduction To Helicopters 101, all you are expected to do is fly the chopper to an airport and leave it. For an easier landing, fly past the buildings and turn around over the water and come back in low. This way you avoid running into buildings.
After you land, you can hop into a car parked there and go for a bite to eat or a nap, maybe stopping to freshen your armor along the way.
As in real life, flying a helicopter in this game is difficult. You have to follow another chopper who will weave amongst skyscrapers and under bridges, and if you fall more than a little behind, you lose.
The easiest way is to get above the buildings so that when your foe twists and turns, you can follow his route from above without bumping into buildings. There's no extra credit for going under the bridge after him, and it is easy to hit the water and die, so don't do it.
When you see him heading for the bridge on your HUD, it is time for you to descend because for Jacob to hit him with a missile, you need to be on or very close to the same level as the other chopper, all the while trying to keep up with him. And this IS a time-sensitive mission because if he gets back over land again, you lose.
The good thing is that if you lose without dying, a cut scene will have you in the chopper back on the ground with Jacob getting out, after which you can take it back up in the air and practice until you get a call from ULP that the chopper is ready for you to take off. You can fly the chopper you are in back to the take-off spot and land and get into the newly-spawned chopper and repeat the mission. You don't lose any health or money or anything for failing, as with many missions.
When you complete the mission, you can fly to wherever you want to go next and just land it on the ground and leave it.