Kingpin's second mission is purely of the vehicular persuasion. You'll be racing three routes, trying to beat the given time. There are no competitors (so no easy wins via taking out your rivals), but the time limit granted is extremely generous- you can afford slow turns and even a crash or two while still completing the track successfully. As with most race challenges, you are given a certain amount of time on the clock, and each checkpoint adds a few seconds.
You race in the Neuron- it's not the toughest car in the Mayhem stable, but it's still a hundred times tougher than any civvie vehicle, so don't be afraid to put some dings in it. The first route is pretty simple- just prioritize control over speed- it's better to waste five seconds taking a turn slowly than waste twenty seconds extricating yourself from from a crash. The only judgment call here is the ramp- you'll want to land this jump back at street level, rather than up on the balcony, so be sure to lean left on this one.
The green checkpoint is the final one in the route- driving through it completes the race.
Race Two is relatively straightfoward- the first part is just drifting corners and city streets (ignore LEGION trucks, cars, and patrols- they're not part of this mission). About halfway through you'll take a turn into the riverbed, but this ends making things easier- no intersections to contend with. You can also collect a crystal en route to the finish line.
The final race starts among some cargo containers, but quickly goes off road. While time remains generous, you'll want to take the ramps here at full speed in order to hit the high-altitude checkpoints.
The final checkpoint is just such a high-flier.
Once you've completed all three, you'll learn a little bit more about Quartermile, and earn the usual Gadget and Weapon Skin.