A quick and simple mission. Head to the local pub, then head around back to find Burke when prompted. After a cutscene, get behind the wheel of Burke's convertible and hit the gas. You'll need to speed, smash objects, and rack up near-misses.
I found that coming as close to other cars was the best way to max out the "fear meter", and that nearly missing oncoming traffic was particularly effective. With a little bit of aggressive driving you'll convince Burke. Pull over and get out of his car to complete the mission.