Like @Glenn_Smith I am truly an amateur photographer, and afficiando, not a working paid pro, though I have sold a few images along the way to folks who tracked me down and parked at my front door.
The question is posted as: What are the most difficult photos to take? It does not ask what are the most complex to create after capture in image editing software, so I am going to limit my comments to the actual act of image capture, not image creation after capture
I truly enjoy seeing the fantastic images created today by photographer/imaging creators with modern cameras and software and computers, but that is an immense field to discuss, and one I know only a little bit of what I have read on the web.
The interaction/relationship between a photographer and his/her human subjects can vary from the dispassionate high school portrait shooter for the yearbook or the tech at the Department of Motor Vehicles, to a deep and significant interaction where the photographer lives intimately with their chosen subject for days/weeks or even months at a time. This can be seen as difficult or very pleasant depending on a lot of other factors, but are not what I am choosing to discuss.
Modern digital cameras are now enabling us to photograph scenes we cannot even see with our own eyes - This runs the gamut from deep infra-red photography, to very high speed photography, and long exposure photography, and finally UV and X-Ray photography.
Modern imaging is truly part of the technological revolution we are all living through.
While I choose to shoot IR at times, and readily shoot long 15 stop ND filters at the beach occasionally, and I shoot high shutter speeds of birds in flight frequently, what I find challenging is the photography of the night sky - complete with very low light intensity, moving objects, and moving photographic bases ( the Earth ), along with varying atmospheric conditions leads to a large field of new things to learn and practice.
I began shooting the night sky with standard photography equipment, fixed tripod, a long lens, and a digital camera with a cable release. I managed to capture lunar and solar eclipses with this gear, but now as I begin to explore this arena, I find I need to make a big step up in knowledge to capture images of planets, moons, and other celestial bodies.
Getting a decent telescope is just a web page and a fist full of money. Even getting a German Equatorial mount is easily available now. What I hadn't really given thought to, is getting access to ground with a great view of the sky in 360º in the mid-west with its tree strewn horizons. I may have to begin to talk to a realtor yet - my yard will be very limiting. What I would love to find is a nice open hill in a dark zone and a good local astro-photography club.
I will have to be satisfied with
l will add more to this post as I progress in my quest