The first special tag that I drew after moving to Montana was for a Mountain goat. One of my co-workers was from Phillipsburg, MT and told me where in the Pintler Wilderness to find one. I waited until late season for the goats to get their long winter hair.
When I finally went, I drove as close as I could to the Wilderness Boundary and spent that night in the back of my truck. The next morning I headed up the mountain. When I got to the divide the snow was knee deep, and I spotted a lone billy several hundred yards down the other side.
I had heard or read that goats rarely look above them for danger, so I dropped my day pack on the divide and started down to get a closer shot. Halfway down to the goat he looked up, saw me and bounded down the side of the mountain in 20' leaps, then went up and over the other side of the valley.
When I started back to the divide, I would take 10 steps up then stop and take 10 deep breaths all the way to the top. I was only 30 years old and in good shape back then.
I got back to my truck and again slept in the back. When I woke up the next morning it had snowed another foot over night, so I went home thinking that I would come back when it quit snowing. It didn't.
Three years later, I had moved to southern Montana and drew another goat tag near West Yellowstone and only 100 miles from my new home.
I made several summer scouting trips into this area, and as the area was also in one of the Montana Unlimited Tag Bighorn ram units, I also bought a ram tag. Sheep and goat seasons opened in early September and I went hunting into that area a couple of times, but I purposely left my goat tag at home so I wouldn't be tempted to shoot a short haired billy. I didn't see any rams on those trips.
By November 14th, I figured the goat's hair would be long enough, so a friend and I took his tent camper and camped near Quake Lake. When we got up the next morning, the temperature was -5* F. My friend had a cow elk tag so I dropped him off one drainage before the one I to go up looking for a goat. When I started up the drainage the snow was knee deep and it took me 3 hours to climb up to where it had only took me 1 hour without the snow.
My climb up was successful and I made about a 100 yard shot on an old, long haired billy.
I gutted him and completely skinned him out where he had fallen. When I skinned him my hands were so cold that I pulled his skin over my hands for much of the skinning.
To get him down, I put his head and hide in my pack and would drag his body to the top of a cliff, push him over, then work my way down around the cliff, then drag him to the next cliff, and repeated that all the way to the bottom.
That hunt was 41 years ago, and I have applied and not drawn for another Montana goat tag every year since.
Now, to get back to the title of this thread "What was the most challenging animal that you have ever hunted?"
In 2017 I went to the GSCO show in Las Vegas and got talked into doing a hunt in Azerbaijan for a Dagestan Tur.
I had my own horses for over 20 years but when I went on this hunt I hadn't been on a horse in another 20 years. The horse back ride to our base camp took most of a day and after we left the valley floor, the steepness of these mountains made the mountains of my Montana mountain goat hunts look flat.
Our base camp was above timberline where they had a little shelter that we could get under for our meals and some semi-flat ground for our pup tents. But after our first hunting day's climb, they decided that we should just sleep on the ground up in the area where we were hunting so I wouldn't have to make that climb every day. One of the guides would go down to base camp at the end of the days and bring up food the nesxt mornings.
We saw Tur every day, but they were either too far away, or on slopes that they said were too steep for me to go on, and if I did shoot one there, it might fall in an area where even the guides wouldn't be able to go.
On about the 4th day two Tur rams fed into the basin where we were. The ridge line of that basin was the boundary between Azerbaijan and Russia.
The rams stopped feeding at 327 yards from us, and after the recoil of my .300 Wby the ram that I shot was tumbling in a cloud of dust down the side of the mountain. Two of the guides went after my ram, and the head guide and I worked our way down to where the draw my ram fell down met the creek below us.
When we all met it was too dark for pictures, so we took these the next morning...