Mew is, of course, one of these. The Generation 1 Pokémon is known to those that have only a passing knowledge of the lore and finding it and snapping it is one of the game's most enjoyable moments.
Here is how you can do it.
Mew appears in the Lental region, in the Founja Jungle map, at night, and on level 2 research.
Mew will only appear once you have completed the main story mission.
Once in the Jungle, you will see a purple orb floating around, pointing your camera at it will not reveal the name of a Pokémon but simply "???".
Play some music and throw a flufffruit at it and continue to take pictures, after you hit Mew three times they will appear at the Ancient Ruins.
There are a few other opportunities to take pictures, once you're done leave the research. You should have a number of four-star photos. You will also gain access to a new "Myth of the Jungle" request from Todd, which will task you with capturing a photo of Mew eating a fluffruit (It's the fruit that looks very like an apple).
Completing the Myth of the Jungle request
If you have completed the step above, Mew will now appear during the day too, and if you enter the Founja Jungle, level 3, during the day, it won't be long until you see them flying around.
You will have to have your wits about you though, as Mew flies around quickly, keeping a careful eye on them is key to not losing track of her.
There is many moments to capture some great snaps of Mew but there is only one time that you can capture her eating a flufffruit.
It happens shortly after you pass a mountainous ledge where sits a Liepard.
As you follow Mew down to the ground level, they will stop and look towards some flowers on the ground, at this point throw a flufffruit near the followers which should attract the attention of Mew who will pick it up and eat it.
At this point, snap away!
You will know you have been successful because you will be commended for your good technique by Todd. You can now head out of the research, open up your LenTalk device, and complete the quest with Todd.