In order to obtain this Trophy you must mount a Chocobo at least once.
The ability to ride a Chocobo is restricted until you reach Chapter 3. Drive to the Wiz Chocobo Post and talk to Wiz himself. He will inform the party that Chocobos are unavailable to rent until a certain monster is dealt with.
This will trigger the ‘A Behemoth Undertaking’ hunt, in which you must defeat Deadeye, a (would you believe it) behemoth. Different to typical hunts, this mark requires Noctis and the group to track Deadeye through a certain part of the world.
Once defeated and the hunt turned in, Wiz will allow Chocobos to be rented. Simply move to the yellow post and rent a Chocobo bird. Once you’ve mounted it for the first time the Trophy will unlock.