This achievement can be done at the very beginning of the game as soon as you have control of Lincoln and can move around New Bordeaux. The video below shows the achievement being obtained in the very early "A Taste of the Action" side mission where we are supposed to drive Ellis to Sammy's. So, interestingly, Ellis is with us for the achievement.
To unlock the achievement, there are three criteria that have to be met:
--Be in a Police Zone
--Be chased
while driving a car for two minutes
--Escape the police zone either in the car you had been driving, on foot, or by getting out of the car and into another one
You must be in the car being chased for two minutes. If you get out of the car before the two minutes are up and continue to be chased on foot, even if the total time in the police zone is over two minutes; the achievement will not unlock. I tested this to verify it.
The below video establishes the police zone by ramming a police car. We could use any car for the chase, but we highjack the police car and use it to get another achievement:
Intentionally staying within the police cordon for over two minutes may result in a significant amount of damage to the car. Consequently, the car you had been driving may not be the best means to escape the cordon once the two minutes are up. You can get out of the car and escape on foot optionally getting into a new undamaged car. In the above video, we drive the car we had been driving into the water. This is, perhaps, the simplest way to escape because the police will not get into the water to chase Lincoln.
The faithful Ellis stays with Lincoln through all the mayhem. At the end of the above video, you'll notice a green dot behind Lincoln on the mini-map. That's Ellis.