Pupperazzi

It can be combined with portrait artist

Word of advice for anyone who was struggling a bit with this one after trying only petting. Through my own personal experience with the game the dogs rarely ever stuck out those tongues with simply petting, so much in fact that I barely had more than half progress on this achievement by the time I had finished everything else. What I did find almost always worked was enticing the dogs with a bit of food items. Walk up to them with any old food item (ie hamburgers and hot dogs, found on picnic tables in muttropolis and mellowstone respectively, or even froggurt from the vending machines) and whip out that camera (with zoom lens if you want to ensure that closeup) for a quick pic once the tongue's out. After done pick up the food item and repeat for skyrocketing progress.

Long story short: FOOD FOOD FOOD is the key.