Some minor spoilers for Chapter 5 bosses/characters
This achievement requires you to get a photo of Gentiana, Luna's divine helper, who starts speaking to Noctis in Chapter 5. Getting said photo relies entirely on Prompto and his random picture-taking.
Gentiana will appear in photos at random, without actually having been present when they were taken. No need to replay her scripted appearances.
However, going from the official guide, there are some requirements and ways to increase your chances at it. First, the picture can apparently only be taken after you have completed the Trial of Ramuh in Chapter 5.
Second, you must be in Lucis, and not any of the other areas you visit. Third, the picture can only be taken between 6:00 AM and midnight. And finally, the chances for the picture to be taken apparently increase the longer your party stays awake. The longer you go without resting at a hotel or camp, the higher your odds are for getting the picture.
That being said, this should easily be gained through normal play. The chances are high enough already. I ended up getting probably 6 or 7 photos of her as I played through the story.
This is all taken from the official print guide for the game, meaning it can be out-of-date if they have updated how this all works by now.
You also don't necessarily have to have your party comment on the photo, just make sure you pick it out of the lineup and look at it full-screen. My first photo didn't spark any commentary from the gang, but I still got the achievement.
Thanks to Allgorhythm for testing and disproving the location and time requirements!