Early Vigilante with the Cop Bike
Lots of bike skill helps, but isn't completely necessary if you are experienced and careful. Still, I wouldn't recommend starting the vigilante mission without at least 50% bike skill.
Vigilante level 12 can be completed with around 2000 rounds of ammo for the SMG; I recommend collecting 2500, just to be safe. SMG skill doesn't make a difference for drive-bys, and the skill will probably be maxed by level 10 or 11.
The HPV-1000 (cop bike) is the best vehicle available early in the game. Since the targets shoot back, it's pretty darn difficult to complete the mission by doing drive-bys with the 4-wheeled vehicles. (GTA_Pheak mentioned that he almost pulled it off once; he had a bunch of homies with SMGs along for the ride.)
Each level completed will boost the health of the vehicle a small amount, and you can't get a flat while driving a vigilante vehicle during the mission, so if you are careful with the cop bike early in the mission, it will survive well beyond level 12 (we can only measure this up to 400%, but it seems to build even higher). More vehicle health is granted for finishing the level while driving the vehicle than while on foot. Plan on finishing the mission with the same bike that you started with, even if you are shooting for level 55.
I never paint the bike during vigilante, all star management is done with bribes. It's difficult to avoid earning a wanted level during the mission. Blowing up vehicles is more likely to trigger the wanted level, but I usually lay as much ammo into the vehicle as I can and hope the explosion takes out all targets. Plan on running with a 2 star wanted level through level 9 (the strategy changes for the final level). Get a map if necessary, and track the bribes (and armor) so you know when you can reuse them. Avoid 3 or more stars if possible because cop bikes and road blocks appear, and these can cause a great deal of damage to the bike.
I prefer to complete vigilante in badlands north of LS (the country side of SF must be the worst place for this mission). There are plenty of bribes, and very few foot cop or bike cop spawns to worry about. I find vigilante much easier in no-ped zones. The are plenty of shortcuts; the game seems to calculate the time allowed for each level based on how far the targets spawn from CJ, and it uses standard bot paths to figure this out, so the shortcuts across a field can save a lot of time.
Level 1 - 8 or 9: The goal is to build a large time buffer, about 8 or 9 minutes, so you have time to break off attacks to refill armor and health, and clear the stars if necessary. Since I know how you are about the races, I would recommend the same dedication to this mission - it's really fun once you get the hang of it. Practice this first part until you can clear the target quickly and efficiently, and the 2 star wanted level becomes simple background noise.
I can't think of many practical suggestions for destroying the cars. Vehicles seem take more damage to their sides than the rear, but I find it safer to stay behind them in order to hide from the return fire. If you aren't in one of the towns, or haven't fallen recently, it's usually fairly safe stop behind the damaged vehicles as the targets bail and finish it off before they can escape from the explosion. Once they are clear from the vehicle, I charge the most dangerous target (shotgun, AK) and pepper them to prevent return fire while I run them over. Then I continue until I'm just out of range of their weapons before I turn make another charge. I prefer to take out the last vehicle and work my way forward one at a time. This tends to keep the other targets grouped together.
The place I usually look to save the most time is during the pursuit. I often find it helpful to mark the position of the targets when they spawn in, and then watch to make sure I know which direction they are head. I want to avoid racing to where they were and then chasing them down to where they went, and instead anticipate where they are going and meet them there.
Level 9 or 10 -12: The strategy changes, and it can be difficult to make the transition. You should have a large time buffer to work with, so don't get in a hurry and die with several minutes on the clock. Clear the wanted level, and get some food and armor. If you take a lot of damage, break off the attack and go get some armor and a snack. You really don't want to be anywhere close to the range of a shotgun, especially if your armor is already half gone.
If you are still having difficulty, then consider using some of that valuable mini-gun ammo. Figure out where the targets are headed, and ambush them at the end of the road. This is much easier with the long roads outside of the cities. If planned well, you should be able to be aimed at the spot where they will first appear, and be able to destroy the vehicles long before they get off a shot. BTW, the mini-gun range is extremely long. With the mouse aim ability on the PC, I can hit anything I can see. For example, from the hill to the east of area 69, I can hit vehicles on the road on the west side of the base.
BTW, mini-gun strategy is a lot of fun for vigilante with the SWAT Van after you finish the game and have unlimited ammo. The SWAT is really slow, and can't even chase down a Washington if it's on an open road. So I almost always need to use a cut-off route, or at least parallel them when I'm far enough away that it doesn't trigger their spook-o-meter.
And if you continue with vigilante past level 12, the mission gets a little easier. It's a lot harder to earn a wanted level after level 12. Sometimes it's impossible to raise the wanted level, even if you want to. I was doing a 6 star vigilante mission with the Rhino, and accidentally ran over a bribe I didn't know was hidden in Foster Valley, and no matter how hard I tried, could not get that 6th star back. Also, the weapons of the targets seems to be fairly random after level 12. You might run into a shotgun or AK once in a while, but generally they aren't the severe threat of the targets on levels 10 - 12.