you should get this fairly early into the game. just go and wreak havoc in free mode (speed, drive off road, cause damage, etc.) or choose the "cost to state" events or any other that involve the cops chasing you. you must escape the police once the pursuit has started in order for this to count as a successful pursuit. try using the police breakers (orange triangles on map) when the police are right behind you to incapacitate them and then try and get to a cool down spot (white rings on map) until your blue meter is full at the bottom of the screen.
do this 5 times and the achievement is yours.