Completion Level: 12
Reward: Maximum armor level becomes 150.
Vigilante missions are a bit easier than most vehicle missions, although not by a whole lot. If you want to get all the way to level 12, load up with a few thousand SMG rounds at Ammu-Nation (there's nothing worse than getting to level 11 or 12 before running out of ammo!), then find any police or military vehicle and click the R3 button to get busy.
The purpose of a Vigilante mission is to track down and kill bad guys; they're represented on your radar with a red blip. When you reach the location of a blip, you'll find a vehicle with a red arrow atop it; as the baddie catches sight of you, though, he or she will start to speed away, so you'll need to engage in some hot pursuit if you want to catch them. At level one, you'll have a car with a single driver, at level two, you'll have a car with a driver and passenger, at level five, you'll have one car with four occupants, as well as a second car with a single driver, and so on. In order to complete a level, you'll need to kill all of the targets, which usually involves getting alongside them and engaging in a drive-by until their vehicle is damaged enough to force them out, then picking them off while they're unprotected. The armament of your enemies will also increase in quality you proceed through the levels, so be ready for some firefights when they finally do duck out of their cars.
There are numerous vehicles in which you can attempt a Vigilante mission; pretty much anything that comes along in the course of your own experiences with police can be used, from a lowly HPV1000 to the mighty Rhino tank. Everything has its own specific utility; although the police bike will leave you open to damage, for instance, you can fire forward on it with your SMG by using the L1 button, which makes it fairly easy to blow up the criminal cars from a distance, without having to come up alongside them (which lets all of the criminal occupants of said cars fire back at you). You can also use the vehicle-specific weaponry of some vehicles to further your cause; the Rhino's turret will make exceedingly short work of your enemy's cars, for instance, while the Hunter attack chopper's missiles can do the same.
In all, the mechanics of hunting down criminals and killing them aren't difficult; you should be able to build up quite a stash of time after your first few missions, eliminating that particular source of tension. What's more difficult to deal with are the other cops; they don't take too kindly to you boning in on their suspect apprehension turf. In other words, your destruction of the vehicles and criminals will get you stars as normal, meaning that you'll have to deal with pressure from the police as you go about and make your rounds. There are a couple of ways to deal with this.
The first is to eliminate your wanted stars as they start to make your life difficult. This is perhaps most easily done through police bribes, but this is somewhat inefficient, since they only eliminate a single star and won't always be conveniently available to you. A better method is to sacrifice a bit of time and make a stop into a Pay N Spray to eliminate your stars. Obviously enough, you can't take a military or police vehicle into a Pay N Spray, but since you can exit your vehicle for up to sixty seconds, it's usually feasible to get out of your police vehicle, hop into or jack a normal car, drive it into the Pay N Spray, and then return your cop car before the 60 seconds are up. (This is especially easy in San Fierro, where you can bust through the upper floor of the car dealership and grab a car to drive into the Pay N Spray. Assuming, of course, you completed the car dealership acquisition missions.)
If you have a police vehicle in need of repairs, on the other hand, you have limited options. If you have a surfeit of time, and a low wanted level, then you can park such a vehicle in one of your safe house garages, let the door close, then open it again; the vehicle should be completely repaired and ready to use. In most cases, though, you can just grab another cop vehicle when you have a small wanted level, as there'll be plenty of them around after a few criminal kills. If you have a Rhino, though, you'll probably find a quick garage stop between every fourth level or so will ensure that you can keep your tank throughout the length of the mission, assuming you don't run headlong into every car you see.
The ultimate Vigilante vehicle, though, shouldn't require any repairs at all. If you can obtain the Hunter assault chopper (by getting all gold medals at flight school), you can use it to easily complete the level 12 requirement for your Vigilante missions, assuming you're decent at controlling it. Since you can fly above any obstacles (or cops), you shouldn't take any damage at all, save for that incurred by bumping into things.