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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 one of the targets from the Most Wanted list for a rundown. Mark their location on your radar, make your way over there, and kill every marked criminal in the area. There of 30 targets; 10 targets in Dukes/Broker, 10 targets in Algonquin, and 10 targets in Alderney. When every target on one island has been marked as deceased, move on to one of the other islands and access a police car computer from there for a new list.
Most often the criminals are surrounded by goons, so you'll want to suit up before attempting these. Get some body armor and a powerful weapon (such as the Carbine Rifle) with plenty of ammo. You must remain in a cop car during the hunt, otherwise you have 30 seconds to get in a cop car before the current mission is failed. If you do fail, however, fear not, as you can attempt any of these as many times as necessary.