Burnout Paradise

I found that as other cars were moving to take me down a quick dab of the brake would mean I caught the back of them and their momentum would carry them across into a barrier or traffic and get me easy takedowns, I managed a chain of 15 with this method. This and Rampage should be easy to get together.

Choose an aggression style car with a high amount of strength, such as the Inferno Van or 4x4 pickup.

Choose a road rage event that allows you easy access to the highway/freeway. The road rage event nearest to your original garage is probably the easiest (you can access the highway via a ramp directly to the south of the garage entrance/exit).

Stay on the freeway in same direction traffic. Be cautious of the AI opponents as they'll often try to force you off the freeway at exits or via shortcuts.

When attempting takedowns, just "bodycheck" other vehicles into other vehicles or the sides. Do not allow yourself to get trapped between a vehicle and the side.

You can repair yourself mid-event if necessary, but chances are if you are getting wrecked before you hit 10 takedowns, it's probably easier to restart the event than to get off the freeway and get repaired.