Among your journey across Shibuya, you'll acquire a multitude of pins that you can master through extended use in combat. Through your successful clearing of combatants, you'll be rewarded Pin Points, or PP, that is used to level your pins up. Most pins come with either 3, 5, 6, 7, 9, or 10 levels that they must progress through. Mastering a pin can either come with an evolution/mutation, or just a clear cap on its preferred point limit, denoted by a star. You'll most likely obtain this through your first few battles with the given pins you have access to early on in the game.
This is also a precursor trophy that ties into further mastery trophies, so you will have a heck of a time avoiding this unlock with the amount of combat you'll have to go through. Do note, however, that this and future mastery trophies require you to master a pin on the Record page. While you will end up developing your pin collection on the Pins page, this and later ones instead track the Mastery progress of pins on the Collection screen. Out of the 333 or so pins you can collect, master, and/or sell, if it is denoted with a Star on the Collection screen, it will count as a Mastered pin for the sake of this trophy.
TL;DR: Level up a pin from 1/# to #/#, earning a Star on the Collections page over this specific pin to get this trophy.