There are a total of 18 events that fall under the Criminal Convoys heading. You can complete a single one of them to unlock the Critical Focus skill, which will be useful elsewhere, and 10 for the Destroyer gun. Completing all 18 nets you an achievement, trophy.
Below, I'll outline the various Criminal Convoys, sorted by region. You can tackle them in any order you like, naturally. Note that most convoys pop up as you advance naturally through the game. Only so many contracts and convoys will be indicated at once, so you may need to take care of contracts if you want to make room for convoys to appear.
Brandon Docks: Caught in the Loop
This is one of the more difficult convoy missions, so don't assume otherwise just because it's listed here first. You have multiple targets for this mission, and your goal is to knock them down rather than kill them, even though that conflicts with Aiden's thoughts on the subject. It's easiest to bump the rear vehicle from behind, then take down the driver as he gets out and hop into his vehicle. Follow the map indicator to your second target and repeat the process, then flee again and (hopefully) get away from your foes to complete the mission.
Brandon Docks: Dockwork
This one is easy. Just look for the line that is traced along the map. You will start a short distance along it, so find a vehicle and go after the convoy. Your target is one of several vehicles, so bump it and that will alert your victim to your presence. You can try using environmental hazards, or just make him crash some other way. It's best if from there you can convince him to leave his car and then run him down with your vehicle, which makes it easier to then flee the scene, but you can also shoot your way out of the conflict, using cars for cover.
Brandon Docks: Lords of the Wards
You don't want to kill your target in this particular mission. You simply want to convince him to leave his car, and then you want to perform a takedown and get out of there. It works especially well if you can perform the takedown just as he gets out of his vehicle, then jump into the vehicle and drive away before his men even know what's happening.
Brandon Docks: No Rules
You need to knock down your target, not shoot him or run him over with a vehicle. Chase his convoy and then bump his car to make him exit. Use a takedown move. The problem is that he travels with a lot of extra protection, so it's difficult to single out your foe and take care of him without first eliminating his crew. You can park your car in front of your enemy's lane at the bridge the convoy passes early on the create, creating a bottleneck. If you employ that tactic, be careful not to shoot your target while you mow down his men.
Brandon Docks: Requiescat in Pace
This convoy mission is the last one you will unlock, and includes a reference to Assassin's Creed IV.
Completing the mission will require either a lot more skill than I seem to possess, or a combination of careful planning and luck (that latter combination being the only reason I was able to persevere). Your target rides in one of three vehicles that heads along a highway, across a bridge and into the heart of Chicago.
You begin a long way from that convoy, so you'll have to spend the first few minutes catching it. Once you do, you have to decide on an approach. Some things to keep in mind: there are Elite and heavily-armored goons with assault rifles in all vehicles, and your target himself is also packing heat. You don't have time to take out everyone if you rush, so you you should focus on using a takedown move on your target and getting out of there. Unfortunately, a second or so is all it takes for everyone to gun you down (and often, much less).
I finally cleared the mission by catching up to the convoy on the bridge, pulling in front of the middle limo like a wedge, using a takedown move on my target, then jumping over the concrete rail and falling to the water below. Then I swam under the bridge and stayed there until my pursuers finally gave up the chase. It was cowardly, but it worked. Good luck to you if you choose to be more noble!
The Loop: The Beast
This convoy is trickier to stop because the primary vehicle is an armored car, fresh from a heist. It will not stop for much of anything except a steam vent. Sometimes, it will seem like it is about to stop, but if you get out of your vehicle, it will start going again. You need to make sure that you deal a decisive blow and see men piling out of the armored car. Then you can run your target down and keep going to evade his friends.
The Loop: Chasing Shadows
This guy travels through a tunnel, so you won't see him if you're trying to track him above ground. All you'll see is an indicator attached to an invisible car. Find a tunnel entrance, then. It's not far from where you start. If you put a waypoint on your target, the game should provide a blue line to direct you to the tunnel. You'll have to move quickly to make up for lost time, but the good news is that you can simply eliminate your target once you find him. You're not required to get out of your car. Just bump his vehicle from behind, then run him down when he emerges from the passenger side.
The Loop: Downtown
This is a straightforward mission. You have to intercept a convoy and take out the target. The easiest way to do that is to use your vehicle as a battering ram. Simply drive directly into your target, head-on. Then get out of the car and use your gun to mow down the target and driver. Quickly hop back into your vehicle and escape in the usual manner.
The Loop: Excessive Force
This mission requires you to take down a corrupt cop who is riding in a convoy of three. You can set a waypoint on the convoy, then run to greet it. Let the first car pass, then get alongside the passenger side of the second vehicle (or as close as you can manage, since it is moving) and press the button to bring up your weapon wheel. That will cause the driver to slam on the breaks. As the vehicle stops, your target emerges. Use a takedown move, then quickly jump into the police cruiser (or run for safety). If you jump into the cruiser, you can often drive it away while your enemies regroup, which puts you in prime position to lead and evade police pursuit, thus completing the mission.
The Loop: Long Division
This convoy mission is another of those that is a pain in the butt for the simple reason that you have to take out a couple of targets, rather than just one. Drive to the point of intersection then ram a vehicle to stop its driver. Start with the one in the rear of the procession. You can take out one goon and then hop in a vehicle and go after the second one, repeating the process once you find him (only this time, you want to follow up your takedown with a bid for a quick getaway).
The Loop: Toll Bridge
In this mission, your target is driving an armored vehicle. More importantly, he's driving it along the freeway. That means there aren't a lot of environmental hazards you can use to slow his approach. The best technique is to quickly drive to the freeway and come at the vehicle for a head-on collision. After you crash, the guys will get out of the armored truck. You can take out the guy on the passenger side, using the truck as a shield from his cohort, then quickly jump into the truck and drive away. As you make your slow escape, the armored truck's benefits are now transferred to you, so it's not terribly difficult to evade your pursuit long enough to drive into a more residential area and take them out with steam vents and the like.
Mad Mile: Militia Mile
This is a straightforward mission. Just intersect with the moving target and take out the vehicle and its driver, then escape. There are lots of steam vents and lights and such that you can use to make the task simple.
Mad Mile: The Quick Fix
At least for me, this assignment is a tough one because you begin in the wrong area to easily intersect your target. I had to drive along a bunch of roads at high speed just to barely make it to my target in time. Once you reach the target, though, just ram the vehicle to stop it from moving. Then take out the target and drive away, easy peasy.
Parker Square: Made Men
This is a challenging mission because you have to knock your opponent to the ground, not kill him. Intersect with the procession, then bump the car belonging to the target. He'll get out on the passenger side, and you can perform a takedown before jumping into his car and getting out of there. If you're having trouble, one surprisingly effective alternative option is to just start running along the rode, along the yellow line that indicates your target's path. Get in front of the car as it gets near, then pull out your gun. Shoot the driver, then use your takedown move on the passenger when he gets out of the vehicle. Then escape.
Parker Square: Parker Pursuit
This is a straightforward mission. Just find your opponent and take his car down (a steam vent works beautifully), then get him when he exits the vehicle. Finally, flee the scene ahead of the other Fixers, and take them out with environmental hazards as they try to exact revenge.
Pawnee: Small Town Justice
In this mission, you'll target two enemy vehicles at once, which makes things considerably more difficult. One vehicle carries a couple of guys who walk around in armor, which adds to the difficulty. I tried a lot of strategies here. What wound up working for me was setting an IED along the road where the convoy travels, then detonating it as the lead vehicle in the convoy passed over it (taking out the two Elite enemies right from the start). Then I ran downhill to the houses I passed on the way up the hill. They provide a lot more cover, and I was able to lead a few enemies around at a time. The guys you are targeting for this mission will be among them, so you can use takedown moves when they follow you around buildings. As long as you don't allow yourself to be flanked, the strategy should work for you also.
The Wards: Into the Pit
This is a relatively straightforward mission, except that your target will absolutely run rather than stopping to have a shootout in the street. You'll have to disable his car (which seems to take more abuse than normal) and then run him over or shoot him. There should be plenty of hazards you can throw in the way of any pursuit, so it's not difficult to escape once you've done the deed.
The Wards: Juggernaut
This is a standard mission, except you start a little further from the route your target follows than is ideal. Race toward it, and pay attention to the mini-map because the blue course the game plots for you if you set a waypoint won't help you take shortcuts. When you catch up to your target, you'll find that he is driving a large truck. It can take more abuse than a smaller vehicle, but continue using the same traffic hazards as usual and you should put it out of commission. Then you just need to take out the driver and escape his henchmen.
NEXT: Crimes Detected