To gain the "Shutter Bug" trophy in Firewatch (EU), you must first reach Day 2 in the story. This is pretty straightforward but feel free to follow my guides for Days 1 and 2 to get through it.
During Day 2, you will come across a disposable camera as part of the storyline. When you get it, press
to bring up the viewfinder. The trophy requires you to fill the disposable camera by using up all of the remaining shots, indicated by the number in the bottom right of the viewfinder. You can do so at any time by simply spamming
until the number hits zero. It's worth bearing in mind that some unique dialogue occurs later in the game if you are still able to take photos, but it's not particularly relevant. Just make sure you use up all of the remaining reel before you complete Day 79 and the trophy will be yours.