After beating the first story mission, you will get a side quest from Yuri asking you to fix surveillance towers throughout the city, and with that you will unlock Thug Crimes (there will be 5 available in each district). It will be the first type of Faction Crime you unlock, unlocking more kinds as the story progresses.
The quickest and easiest way to get this trophy early in the game is to do all 5 Thug Crimes in Central Park (fixing the towers make them a lot easier to locate). Central Park is the big grassy area in the middle of the map.
Central Park's only Faction Crimes are the 5 Thug Crimes. The larger districts have extra crimes that aren't available until later and you would have to progress further to unlock them.