To obtain this, as the achievement states, you must finish all of the levels in "Sheriffs Hot Pursuit". In order to access the Sheriffs Hot Pursuit levels you must finish the Sheriff's Chase race.
You can access the Sheriff's Chase race (to open up the Sheriffs Hot Pursuit levels) in Chapter 3.
The Sheriffs Hot Pursuit contains a total of 15 cars you must "pull over" to complete. There are 3 cars per level and 5 levels. Each one gets harder as the levels and cars progress.
To "pull over" a car you just need to follow it. The closer you get and the longer you follow it a meter will start going down. Once that meter is completed empty you have "pulled over" that car and your on to the next car.
If you do not follow close enough or slow down the meter will start to regain back to full again. If you get too far away that car will get away and you will have to retry again.
Some of the later levels and cars can be hard, I had to do several retries. I would suggest using the cheat codes (you will still get your achievements). I recommend only doing "VROOOOM" and "IMSPEED" since I am not sure if the others affect achievements and they will not help you at all. The cheat codes are found here:
http://vgstrategies.about.com/od/xbox360cheatsc/a/CarsC....htm