Hi there! I just completed Car Chase on Legend difficulty after around 10 tries so I wanted to share some tips.
An universal tip is that you deal the most damage aiming for the center of the circle, so don't bother aiming for the head of the bad guys.
The first part of the chase is fairly simple, you should be able to complete it with some minimal damage/no damage after a few tries. All my losses were from the truck part so let's get to that:
1st Phase: The easier of the lot, you can only shoot 2 out of the 3 guys on top of the truck. The screen will change after dealing half bar of damage to the left guy or after killing the middle one. While killing the middle one is fairly easy (and you absolutely should do that since he can damage you in the next phase aswell) I suggest splitting your damage and get as close as possible to the half hp mark on the left guy before offing the middle one.
2nd Phase: Quite difficult, but this is where I can give you my most valuable tip. Killing the guy on the truck switches to the next phase immediately so going in for the kill while managing the cars behind the truck seems like the obvious way to go, but if you're here chances are you take too much damage or die while doing it (like I was xD). The thing I noticed is that the cars do NOT actually respawn indefinitely as they initially let you think. So the safest way to proceed is to just kill all the cars while ignoring the dude on the truck and only shooting his rockets. After the truck switches side of the road you're pretty much half way through the cars so keep removing them and finally, once they're over, you can take all your time killing the rocket man. Doing it this way I managed to not take any damage in this phase for the first time ever and winning the run afterwards.
3rd Phase: The hardest one. The concept is the same as before: killing the guy on the truck switches to the next phase and the bikes do not respawn indefinitely (there are about 3 for each of the two positions). You can keep killing the bikes off, while trying to not let the guy on the truck shoot, until they are over (which is what I did) or try to go for the kill of the truck dude after a bit, since all the damage you dealt to him in the 1st phase was retained.
4th Phase: I've seen people stop the driver's attack midway but honestly I cannot tell you how to do it. It seemed to happen quite randomly (mostly didn't) even with every shot on target. So the best thing you can do is capitalize on all the hp you saved from the safety strats we did during the run. If you shoot well you can get away with just taking one hit from the truck, otherwise two. He hits for 50% of your car HP if you hide into it or 50% of Kiryu's HP + about 20/30% of your car HP. The strat is simply to aim well, use Heat eye when he gets close to you and take a hit or two depending on your hp situation. Having 50%+ of Kiryu's Hp and 80%+ of your car HP by this point will make this very safe, just take a hit to both of them and you will have plenty of time to kill him. Otherwise take a hit where you will survive and just unload and pray it will be enough.
I hope these tips will be helpful to anybody having problems with this nightmarish stage. Good luck and, if you fail, just keep trying and you'll eventually get it!