Into Uncharted Territory - Hammerhead
First Available: Chapter 8
Other Requirements: Patch 1.12 or higher installed (Or own Royal Edition DLC)
Location: Hammerhead Station
Rewards: 1,200 EXP & Upgraded Vehicle
This quest begins by inspecting a blue print near Cid at Hammerhead Station. In order to begin this quest you'll need the Royal Edition DLC for the game.
To get into this quest area you'll have to find a small opening between two really large rocks and squeeze through them. Inside you'll have to search for all four of the tires we need but it isn't too difficult considering how large they are and how much they stand out.
As far as enemies go, you'll find Cactuar enemies throughout this area, I recommend using Prompto's Tech Piercer ability if you're having trouble hitting the Cactuars. This ability has a guaranteed chance of hitting and it also triggers a short "cutscene" where Prompto and Noctis are invulnerable to damage.
If you still need help finding the locations of each tire, I recommend you use my screen shot below for additional guidance.
With all four tires in hand return to Cindy and speak with her to turn in your quest. The tires will make your vehicle look rather dorky - however you'll gain the ability to take it off road which makes up for the poor looks. Don't worry, when you complete the next quest and upgrade your vehicle again it won't have the terrible "lifted" look that it does now.