Jump on to any car, preferably a civilian car since Agency cars will often stop to fight Cell, and Cell cars will stop immediately to kill you. Even the civilian cars will stop for a moment once you jump on to them, but once they get moving, shoot the ground in front of the car. The person in the car will panic and drive faster for the next few seconds. Keep shooting periodically to keep them driving fast.
Once you see another car coming, do a small hop (don't hold A, just tap it) so you don't miss and land on the next car. It's best if the second car is coming towards you, so you land on the hood. The second car does not have to be going very fast, but it is better if it is at least moving, just to be safe.
Thanks to "moose0030" for the tip: If you have the Toy Box DLC, you can use the thrusters in order to have more control over your jump.
"Tarzakul" added this to the above tip: There is no time constraint between your jump and the landing. You could potentially jump from the first car and travel halfway across the city (with thrusters) to the next one, as long as you jump from one car and land on another one, no matter where it is or how long it takes.
As noted in the video, you can do this in co-op, that way you don't have to rely on the inconsistent AI driving skills.
Here is a RoosterTeeth video, in case you want to see it in action (this is in the demo, so the achievement looks kind of weird.):