While using the bus in the dare levels during a race, just push the other cars to build up hit points
Demolition Derby
Drive around avoiding cars until there are less than four cars remaining.
Suicide Races
Stay to the inside of the track to avoid the oncoming onslaught of cars.
Turnaround Races
Drive past the turnaround point until it says 'Get back on track'. Press Select to put yourself in the opposite direction (it is faster). Tapping R2 (emergency brake) and going to the inside all the way to the grass is the easiest way to win a Turnaround race. Going in the grass on the inside line to helps you avoid oncoming traffic