This is a Gravina Crime Family mission.
"You're getting so close to Big Sal that you can smell his pomade. But first things first. Each of the three capos in Sal's gang tried to have you killed in prison. It's time to pay them back, with interest."
This might seem like one for an epic firefight, but it's best done as an assassination mission. Each of the three capos are surrounded by as many as ten gangsters, plus others will spawn, flanking you from the sides and behind once the shooting begins.
For the assassination approach, the K98 Rifle rifle is the weapon of choice; the M1 Garand will work, though it doesn't have the stopping power of the K98 Rifle and might take more than one shot. Whichever you choose, both can be bought from Harry's Gun Shop if you don't already own them.
Though you can do these in any order, the expedient way is to do the plaza first, the pier second, and the church last.
Drive west out of the park and turn north. Note that your GPS may switch to the pier location momentarily as you exit the park but ignore that one for now. Head north and just before you get to the Grand Upper Bridge, across from the parking garage, you'll want to turn right and drive down the sidewalk. This is the fastest approach and offers the easiest escape as well. Before you get out, park your car so it's facing the direction you just came for a quick getaway. They won't suspect anything until they see you with a weapon or you open fire, so take cover at the top of the steps and pull out your rifle. The capo is the one with the large green arrow above him, so take him out then immediately get back in your car and speed away.
Head to West Side following your GPS. Just before you reach the Body Shop turn right down the alley and follow that around. This one may appear easy, seeing as he only has about five gangsters with him when you get there, but the moment you open fire they will come in from the north and south to quickly surround you. Get close then get out and take cover by your car. Again they won't react until they see you with a weapon so take aim and kill him quickly.
Seeing as he's standing in a small nook, he has nowhere to run should you decide to have a little fun and run him down with your car instead. Either way, once he's dead speed away to the location of the last capo.
Drive to the final marker at the church. As much fun as a gunfight in a graveyard sounds, this is once again a difficult battle to get through so stick to the assassination plan to wrap up this mission. Drive your car through the front entrance and go over to the left. Get close enough to get a decent shot but keep some distance to allow your escape. Again, try to park facing the direction you just came to speed your exit. Once this last capo is dead drive back to Lincoln Park to end the mission.
The Epic Firefight
If you chose the epic firefight method, come with every weapon you can carry and make sure you have the full allotment of ammo for each. The best advice is to keep moving and don't stay in any one place long, as they will keep spawning and flank you within a few seconds. At this point it's unknown if they actually stop spawning so keep that in mind as well. Always take out the capo first; that way if you get overwhelmed you can always give up and escape. You also won't get through without getting a four-star wanted level so be prepared to battle countless police as well. Remember you can stop between locations to replenish your health as needed, as there's plenty of time on this mission. All in all this is a very difficult approach but if you're playing on easy, or just damn good, you may actually pull it off.