There is only one Demolition Derby activity which has 6 levels and is located at the stadium on this map:
Map no longer available, sorry.
You start off by choosing a car and you can customize its speed and its offensive and defensive features (such as huge shovels or extra framework for your vehicle) As you progress through the levels you can add more things to your car.
When you start, try to ram the other cars health down as much as possible possibly even being the one to cause the explosions - you will get money for causing damage and you will be required to fulfil the specified amount of money and keep your car alive. The bigger the crash though, the more dollar you get. Try to use the LS button to boost when ramming cars also for extra damage.
Doing this in Co-Op will make it easier as your money is combined you don't both need to stay alive to complete the level.