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These missions are available following “Crime and Punishment” in Faustin's mission line. You'll need access to a police car computer to start. For easy access to a police cruiser, first dial 911, wait for the passenger to step out of the police car when it arrives, then enter from the passenger's side to oust the driver. You must come to a complete stop to use the computer. Select the “View Current Crimes” option from the computer menu to view a few crimes. There are three types of crimes; criminal on foot, stolen vehicle, and gang activity. By far the easiest to clear is “criminal on foot,” since you're only dealing with one guy. The other two are a bit more involved; for stolen vehicle, you're up against a car full of criminals, all firing at you; for gang activity, you're against a group of criminals out in the open, but their combined fire can be deadly.
After you have selected one of the current crimes, there is a time limit (visible in the top-right corner of the screen) to reach the crime scene. When you do reach the scene, however, the timer disappears. All of the crimes are taking place relatively close to your current location, so the timer shouldn't be much of an issue. You need only complete 20 of these vigilante missions to both earn 100% completion and unlock the “Clean The Mean Streets” achievement on the Xbox 360 version. You can continue to fight crime once you have completed 20 of these, though there isn't much point then.