Just finished this on hard last night so thought I would add a few tips here for anyone struggling.
First of all don't try and do this straight away. For a start you will need to upgrade your salvage levels on all your vehicles so you might as well do that first. If you want to get a feel for the campaign do it on medium but you will be doing it all again anyway so its up to you if you want to repeat yourself.
As for the actual campaign, my best advice is try and use hit and run and long range tactics. Mortars specifically are your greatest weapon. If you use the combo down-down-up (fire machine gun) you will fire 4 mortars making a firestarter. This is a powerful attack that will set enemies on fire if it connects close enough to them.
I spent the majority of the campaign just driving around away from enemies looking for mortars. The only time you want to move in for some close up damage is when you have a shield. Shields are extremely useful and shouldn't be wasted. For example, if you spot a shield but there are no enemies about, wait by it until they are closer before collecting it. You don't want to waste half of the shields time driving to the enemy.
Radar evasion and damage multipliers are also both useful but i wouldn't say either are a priority.
When you are going in for some close up damage, try and make use of the some of the combos. For example, the cannons buckshot fires six at once and is absolutely devastating. (Up-Up-Down-Fire Machine Gun). The Bullseye Rocket's Stampede special is equally devastating as it fires 5 rockets at ones (Up-Down-Up-Fire Machine Gun) Combine this with the right special, such as on that does continual damage like Beeswax, Boogie etc and you can take half an enemies health off or more in one attack, a few wammies really pile on the damage. As soon as your shield starts to flash get out of the area as soon as possible. Continue searching for weapons. Cannons and rockets are the most effective close up weapons, missiles are ok but are best used from a distance. If you get a good vantage point, such as the top of the ski resort or dam, and your enemies are below you, park on a ledge and fire the missiles as quickly as possible, your should get some solid hits.
For the boss rounds, when your last enemy before the boss is low on health try and stock up on mortars, get 36 if you can.
The physics engine in the game is terrible, especially for the smaller cars, just firing a mortar can send your car spinning out. Its annoying but you just have to try your best to deal with it.
Finally, keep your health topped up, if it gets down to around 50-70%, make looking for a spanner a priority, try and remember where they are on the level. They will respawn but I think its only a limited number of times.
If your are stuck on a specific level PM me and will try and give you some advice.
This game has got 'removal from marketplace' written all over it so try and get the online achievement as soon as possible while the servers are still up.