Actions Speak Louder Than Words
The mission is pretty straightforward. After you blow the bomb, don't go rushing in. Use your sniper rifle to pick off the enemy.
I Need Your Clothes...
This is a motorcycle chase mission. The funny thing is that if you fall behind, the target tends to wait on you. Also, as in all chase or follow missions, you do not have to actually follow the same route; you can run on parallel streets and often the target actually doubles back and/or crosses the street you are on.
It is more important to avoid crashing than to try to stay right on his tail. Before going to the yellow marker that starts the mission, it is always a good idea to bring up the Pause Menu Map to see where you are so that if the mission is difficult, you can come back on your own to look things over and practice the route.
It is unlikely that you can take hit the target with automatic weapon fire at the start; you will just be increasing the probability that you will crash. Your best bet is if he doubles back onto your street just ahead of you; otherwise, it's going to be a long mission.
Each run of a mission involves random factors, and some require some luck to win. All you can do is keep trying.