When competing in the checkpoint events, you should watch the map 
and try to set up as many head-on collisions as you can early on, 
while the oncoming traffic is still packed tightly together. This 
will extend your time clock, and give you an opportunity to slow 
down a bit so that you can line up future head-ons with greater 
precision. Late in the game, if you have to keep your speed high 
just to make the next checkpoint, you will likely miss a lot of 
your intended target vehicles. 

Use your handbrake (right shoulder button) a lot when running the 
arena events. You can dance your car around in a very tight space 
and line up a lot more front-end collisions this way. Running at 
high speed around the perimeter will seriously reduce the opportunity 
for good hits. 

In the game's early stages, when you are still driving a fragile car, 
try to establish the points lead quickly, and then set up a massive 
head-on collision to kill yourself. This effectively ends the race, 
and doesn't allow your opponents the opportunity to catch up.