In order to get a photo of Mew, you need to disable its sheild;
First Mew will fly in front of you. You need to throw three Pester Balls at it in order to break its shell. after that it'll get its sheild back and become much more agile making it harder to take a picture. Then, Mew will appear from behind chasing it's sheild. Hit Mew and he'll spin and you can finally take a picture of this elusive Pokémon and then it disappears