Finish in third place or higher in all five events in a car to unlock re-inflates. You'll need to have these equipped for this achievement.
A very fast and easy place to get this is in "The Hunted" Ambush event. At the very start of the event, drive to the roof and jump off. This takes about 30 seconds and that's where you'll find two spike strips side by side. Run over one, turn around, and run over the other.
It's important to note that if you quit or retry the event, these won't count. So let yourself get busted to save your progress. Start the event again, and repeat until you've got 5 and unlock the achievement.