Submitting this solution because I think it's the easiest I've seen out of all the one submitted here. It is inspired by M0nsterXEnergyy's solution for the "Hazardous Hangtime" achievement: Solution for Hazardous Hangtime in Crackdown
You don't even need any DLC nor to even drive at all. All you need 4 star driving (for SUV jump) and the agency garage. Simply jump in place with the SUV, land on your back, and correct yourself in the same direction as the jump to do a barrel roll. Repeat 6 times.Detailed Explanation:
Get the agency SUV and don't leave the spawn area. The spawn area is an elevator so it counts as being "in the air" when the car is flipped. Pick a direction you want to do a barrel roll in (left or right). Hold B and release to make the car jump and then press the direction stick in the air to make the car flip and make sure you land exactly upside down. Wait a few seconds upside down and then press the direction you want to continue the barrel roll in on the direction pad and while doing so press A to right the car. If you did it right, you'll get a notice that you did a barrel roll as well as some driving skill points. Repeat 6 times. I found this out to be the easiest and most controlled method for doing stunts for this achievement. You should be able to mess up a jump or two and still make it, though once you get the technique down you'll be able to do 6 jumps in a row with no problem.
You can also easily knock out the "Hazardous Hangtime" achievement while doing this obviously, just make sure you wait 6 seconds while upside down: