Once you reach chapter 4, Gentiana will start talking to Noctis.
She also appears randomly on Prompto's random fight photos. Level up prompto's skills to increase the number of pictures he takes in battle. Eventually Gentiana will appear on one of them, so you have to check your pictures at the end of the day and browse all of them.
Beware she can be on the picture but hidden by Noctis or another fighter.
There is another way
*** Spoiler - click to reveal ***It is said that as her identity is Shiva, you can get the trophy if Prompto takes a picture of her. I could not veriffy this though.