I've got the first 7 on the list, all DIY. That said I've never been too overly impressed by lots of different species on the wall. Usually that just means somebody has a lot of money and not necessarilly skill. I'm usually more impressed by the kind of hunters that go out and take quality animals, on public ground, DIY, year after year, even if they only ever hunt the same species.

I have only taken four out of the ten animals listed.

Whitetail & Mule Deer
Black Bear
Elk
Antelope

I do not have the desire to hunt any of the other animals listed.

Ive only got the deer, floridas out of luck on the big game hunting, but i guess we make up for it on the saltwater fishing.
Does the "Hillbilly 4" count? Hog, Squirrel, Possum and Coon

Everything but the bison and the mountain goat. Went on a bison hunt with a buddy was like shooting a cow in the pasture, so I don't think I'll do that hunt. Mountain Goat i have no desire to take one. I"m an elk hunter that's my one thing I'll choose to hunt first everytime.

Why didn't bighorn sheep make the list?

I have the first 6, all do it yourself except for moose.
Redclub

I have deer(mule deer and whitetail),antelope,elk,black bear and cougar and if Montana would ever give me the tags I would get the rest.
BBJ

Bighorn sheep is on the list, ie...."Sheep"

Depending on your bison hunt, i hear those utah bison in henry mtns can be a tough hunt.