I believe i have found a way to grind this out instead of just hoping each day that Prompto takes a bunch of pictures. I completed the game and wasn't very progressed with this due to the fact that I never camped in order bank my xp. When I was finishing up the last little bit of progress for this achievement, I was so tired of running around each day doing random stuff until Prompto had taken 15 pictures. In other words, I got tired of the normal, luck based way of getting this achievement. Here is an easy grind method to get this if you want to get the achievement faster.
Go to the Wiz Chocobo place, not too far from Hammerhead.
Find the pole where it asks to take a photo, and get the photo.
Right by this photo op, are some chocobos. Pet one.
Thats two pictures in like 20 seconds.
10-15 secs are wasted on resting.
Go to the caravan and spend a measly 30 gil to rest.
So every 30-45 seconds or so you can get a few pictures
You should get 2, sometimes 3 or 4 pics if Prompto takes a few random pics, for 30 seconds of work. The max level is 10 and I grinded the last half of level 9 in like 20 min doing this. This is a guaranteed, faster method. You don't have to play for 30 min hoping you get 10-15 pics, instead you can easily match that and beyond with this method.