1) Complete the main story.
2) Reload and use the nearby dormitory to return to past Lucis.
3) In past Lucis, you should already have two of the three parts necessary to get the Regalia Type-F. These are spoil key items you would have obtained from taking down the forts the Empire had set up in Duscae and Cleigne. The only one left, which isn't available until you complete the main story, is in Leide. Up in the far northern corner of Leide, near the hunter's encampment and Keycatrich, is the third and final fortress you'll have to take control of. It's more of a battle blitz with empire soldiers as you will be fighting a lot until it is yours to claim. But once you've done the brawl with all of them and destroyed the generator, you'll receive your third and final key item.
4) Return to Cindy with all three items in tow to receive the upgrade to the Type-F.
5) You must now start driving and activating the Type-F's mechanics. Get enough speed behind the control (while driving Manual) and then take off. Once you're in the air, find a long enough strip of road and start descending towards it until it gives you the option to land again. Line your car up with the road and once you've touched down, park and exit the vehicle. The trophy should pop shortly thereafter.