There's a total of 40 street crimes you'll need to complete to unlock this achievement and they'll be available from the Traffic promotion onwards. The only way to receive a street crime is if you're in a police vehicle. While driving around from location to location the KGPL will call in via your radio and notify you of a crime in process.
When his happens, press A Button to take the crime and a little running man icon will now show up on your mini map. Simply head over to it and complete the street crime for it to count towards the 40. If you don't get them all while playing the story, don't worry. You can go back into free roam at any time and complete the ones you missed.
Certain street crimes can only be accessed when playing through certain desk cases and times in the game.