This trophy unlocked for me in chapter 7 after the Territory Contest case but I'm not sure if it can be obtained earlier than this so I'll just use the method I did it with.
To begin, a popularity event is an extra dialogue scene where you interact with a person or Digimon that you've taken on a Territory Capture, Domination Battle, or post-game Abyss Server case with. The list of 15 partners ranges from other Hudie members to Digimon allies and the few major characters in between however they aren't all available from the start and the Digimon mostly need to be "unlocked" by completing their respective cases near the 3/4 mark of the main story.
When your partner talks to you after the event you are given three options of dialogue. One of them is the "right" option and will give you this trophy and a point towards Someone Special OR Partner Only to You (depending on who you brought, human or Digimon).
If you do a Domination Battle you may find out that there's no option to talk after the battle so I suggest you either do Territory Disputes only OR skip these two cases entirely then do them all in one sitting post-game with the character of your choice.
The first event happens automatically after the first Domination/Boss (Territory Capture) Battle. The second event will appear after 4 more cases of Domination/Territory, OR after 2 more battles
if you give the correct response. The third event will appear after 5 battles OR after 3 more battles
if you give the correct response.
It will take a total of six battles to get all three of a character's events if you get all the answers correct. It will take ten battles if you get all answers wrong.
In my instance I took Chitose along for my first Terrirtory Capture against Tokyo Shock Groove. After defeating the boss Chitose mentioned something and I selected the appropriate response which made some hearts appear and the trophy popped shortly after.
Since the list of applicable teammates and dialogue options for these is in the double digits I'll just leave this link to give you the exact responses:
https://gamefaqs.gamespot.com/ps4/207680-digimon-story-cyber...