Ruff Rider
This should be fairly easy, so no armor boost is needed.
After talking to Dwayne's ex and her new guy, don't waste time shooting her, just hop on the cycle and go straight down the road.
The key to these chase missions is to avoid crashing and just go fast enough to keep up with the him and slow down for corners. Eventually he will crash or stop. How long this takes is a luck factor of the game. With any luck, the chase/mission can be over in less than a minute.
Shooting while chasing in a car or motorcycle is difficult, leads to crashes, and brings the cops, but try it if you wish.
If he crashes, you may want to finish him with a bat or knife to avoid attracting the police, but losing them is easy enough if you prefer guns. Be sure to pick up the money before you take off.
The mission is not over until you go back to Cluckin' Bell to give the money to Dwane, who is a blue dot on your HUD.
Undress To Kill
Easy mission, but use a bat or knife.