The internet suggests it's a fake (they're posed like they shot the beast down). As is this one:
Supposedly, there was an article in the 26 April 1890 edition of the Tombstone, Arizona Epitaph about two cowboys shooting a creature with leathery wings like a bat and a head like an alligator. They dragged it back to town and nailed it up to a barn, its wingspan covering the barn's entire length.  It may be related to a similar hoax about shooting down a Thunderbird that supposedly haunts the American southwest.