The description for this achievement is wrong. You must win the race, not just complete it.
It's a race with checkpoints as well as a timed bomb on the car. At the checkpoints, there is a line of explosive barrels across the track. You must hit and blow up at least one barrel as you cross the checkpoint in order to proceed. The other drivers will bash into you as you pass them if you are close enough.
I tried to legitimately win several times, but I was either getting pushed off course by the other drivers or the exploding barrels would spin me out or knock me off course if I didn't hit them just right. The four cars I raced against to get this achievement all had exposed red gas tanks in the back of the vehicle. I had upgraded Max's ammo belt at least twice so I carried more ammo for the shotgun. At the start of the race, I just used the shotgun and destroyed all of my opponents by shooting the gas tanks.