In order to unlock the Regalia Type-F Modification, you must first beat the story (finish all 14 chapters and defeat the end boss). After beating the story, you can visit a lodging and call Umbra to visit the open world and mop up everything you haven’t done in Final Fantasy XV.
How to Unlock Regalia Type-F in Final Fantasy XV
Step 1: Infiltrate the Formouth Garrison in Leide. When you go near the Garrison you’ll see a new side quest called “Formouth Garrison” popping up. You can do this as early as story chapter 8 but the enemies are level 50+. It would be best to do this after the story when you’ve grown stronger (and you can’t unlock the Regalia Type-F until after the story anyway, so no point in doing it early).
Step 2: After finishing the Formouth Garrison, you’ll receive an item “Strange Engine”. This triggers a new side quest “Into Unknown Frontiers”. All you gotta do is deliver the part to Cindy at the Hammerhead outpost. There are actually 3 of these strange parts, but two are unmissable story unlocks (Warped Wings from the Garrison in Chapter 5, Unstable Stabilizer from the Garrison in Chapter 6, Strange Engine from Formouth Garrison Side Quest).
When you’ve done all of the above Cindy will upgrade your Regalia with the Type-F modification. A fancy batmobile-styled car that you can fly like a jet. To unlock the “Regalia Pilot” trophy / achievement you must put it in manual drive, gain some speed and press Circle (PS4) / B (XB1) to take off.
The only disadvantage is that you can only land on streets. Landing on terrain will crash your car and result in a game over screen. It is a lot of fun though and makes navigating the world quicker.