"The Fuzz Ball" is the final mission for Luigi. Complete "Pump Action Pimp" to unlock it. Before you start the mission, go and get a coach from the depot south of Joey's garage. This will save you time when you start the mission.
Once the mission starts, drive around and pick up all the girls (start with the ones up north and make your way down south). You can pick them all up in one go and should have plenty of time to spare.
Once you pull into the mission marker, watch as all the girls get off the coach, walk into the open door and fall over... then the trophy should pop.