If you prefer to watch a video instead of reading the guide, feel free to do so. There is a playlist that covers every trophy on my YouTube channel. If you'd like and subscribe or even become a member, it would mean a lot to this channel!
In our first shift we can only report parking violations and call for the tow truck. The latter allows us to make progress that matters in terms of trophies. Apart from that it's our goal to reach service star 3 to get access to a patrol car.
Assuming you unlocked the patrol car in the previous step, we now start a shift with a car icon. Starting it in Chester gives us full access to the entire area. Our goal is to force DUI-based arrests and find someone with an open warrant.
The reason I recommend Chester again is because there is a perfect spot to farm speeders. The ambulance trophies can also be done on any other shift where we are allowed to use a patrol car.
The remaining trophies can be unlocked by just starting shifts in the three areas we haven't been to yet. If you get a shift with a car, you can try to total it which ends the shift immediately. Otherwise you have to just stand in the office and wait for 15 minutes until the shortest possible shift ends.