Got my Black Bear rug back. What's the best way to secure it to a flat wall?

I used some small tacks and it worked great.

The taxidermist should have put rings on the back of the head, tail, and each paw to hang from nails in the wall. Ideally, I would want those sewn through the felt, any padding, AND the hide to effectively support the weight.

Rings or nails will work but they aren't necessary. Go buy a package of sewing needles, They are hard steel, and won't bend. You can hammer them through the skin in the sheetrock at the appropriate angle and they will hold. You can use as many as it takes to secure it,they are cheap and it will do minimal damage to the wall.

I used a staple gun in the past. Worked fine, minimal wall damage when I moved/sold the house.

Never would have thought of the sewing needles. Great idea, thanks Jerry.

I made up a flat "mannequin", using a 12" x 48" piece of plywood for the body and 5 strips 4" wide and various lengths, sticking out in appropriate lengths and directions for the four legs and the head. I attached the hide to the framework using black upholstery-type nails, and then just hung the whole thing on the wall like a giant painting.

Works well, easy to build, easy to move when required, and doesn't turn your wall into a pincushion.