Well, driving next to the cliffs should usually work. If the helicopter is too far away, it will probably dodge the obstacles. So it's not a bad idea to let it come close enough to shoot at you, and then try to drive close to obstacles that are high enough to take it down.
Aim-nein missiles work too, at least when you're on top of a hill and the helicopter is coming uphill. You should be able to get the missiles from the previous mission, I think.

Use a turreted weapon. Also, if you get mortars working (see the workaround thread) Mortar damage doesn't have a ceiling, so if you lob a shell under it, it will take damage.

After playing the mission, I'm reminded that those weapons probably aren't available to you yet.
The helicopter uses a turret and missles, which require your engine to be on in order to lock on to you. Turn your engine off and coast to avoid most of it's fire.

This mission is definitely one of the harder ones in the game. I just reached this scene and remembered why I hated it the first time I played the game through so many years ago. I had to redo this level again and again and again... And once again I'm struggling with it!
There's way too many cops, and they all have turret weapons. I remember one time just parking my car in a barn and shooting them as they drove by.
Any tips for dealing with the cops? I'm using a 20mm cannon, the aim-nein missiles, and a rear 50mm machine gun with oil slick. I'm not having much luck with the missiles as they don't seem to be heat-seeking like they're supposed to.

Shutting your engine off makes the police turrets also not track you. Happy hunting!

I recommend just driving around a lot, and reinforcing the armour in the front and back of the car. I think I used two firerite rockets in the front and one aim-nein missile in the back. Two rocket sets are good for taking someone out quickly, and missiles that hit the cop cars in the front do some nice damage. But usually you're better off just driving around and hoping that the cops roll over and explode.

This mission can be a bit of a bitch, what I do is I don't even wait for the cutscene, as soon as the cops are in visual range I shower the first one with gunfire until it blows up, then immediately turn off the road and head along the cliff to the north. You'll find that there's kind of a circular mesa not too far north with a tiny canyon that loops all the way around it. Go back into that canyon, and if you do it right, the police helicopter (which approaches from the east) should fly right into the cliff face on the other side of the mesa. After that, I use this area to retreat to after hit and run attacks to try and whittle down the cops.

These are some good tips, I'll have to try them out later.
Gasbandit's name brought back images of the dream-sequence mission with Patriot, Road Knight, and Gas Bandit. A creepier trio in a video game would be hard to find, but the comment from Road Knight when you snuff him out is great, "This suuuuuucks!"

In the past I found that using the hand gun to shoot out the window worked wonders. You have to hit where the driver would be in the other car pretty dead on, but a hit means a head shot and a kill.
Plus this lets you salvage the most out of the cars at the end, sine the gun does little or no damage to the weapons and chassis and so on.
Unfortunately this won't work for the helicopter as you only shoot only a flat plane, unless you have figured out how to tip the car upo and drive on two wheels!

Psst.. their condition has to be red before the pistol kill works, and it takes 5 pistol hits.

You don't need to inflict any damage to the vehicle in order to kill the driver with the pistol.
Also it only takes one (very) well aimed shot.

That's where I got my handle ;) And the "This SUUUUCCCKKS" was Gas Bandit ;) Road Knight's death line is "(giggle)... Adieu!! (hysterical laughter that turns into screaming and then a death rattle)"
"VIXEN... I can SMELL YOU...."

I just did this mission with 50.cal at the back. and dual 20mm cannon on top. where you meet the 1st bunch of cops. shoot at any one of em. shut off your engine and head left. there is a hill you can hide behind there. Get one down to red by keeping your car moving and having the engine off as much as you can. once he is at the red. shoot him with your hand gun. Helicopter will come. Then stay close tho the high wall next to that hill. helicopter will crash into it. Did test it a few times. And he did crash there every time after he had circled around 1 or two times. Now getting to the end... yeah GL with that.

The vehicle has to be red, meaning it took at least one damage to internals. Could be from flamethrowers, could be from ramming, but the car has to be red.