Carmageddon: Max Damage

This was my preferred method for completing these events. It basically boils down to just continuing to ram into the 5 opponent's cars until they explode. They won't respawn in this mode, so each one only has to be destroyed once... it even counts if they kill themselves or each other.

If you prefer racing through checkpoints and don't enjoy smashing opponents or just want to make it as fast as possible, wait until you unlock bigger vehicles.