This is already pretty easy to get just by going into a parking garage or lot and popping tires, but if you want an arguably faster (and definitely more fun) way of doing it, here ya go...
It seems this achievement also counts tires shot out by the chain gun in the Spider Tank trip. When you pop in just aim low on cars and spray them with your chaingun. Just keep riddling every car in sight with bullets, and this should pop in no time. I did one trip in there that I only stayed in about 2 minutes, and by the time I came out I was only one tire away.
As with many of these achievements, you can use the XBox One's achievement app to track your progress and see how many you need.