Just cut out some 2X2 X 1-1/4" stock, or there abouts, cut a 7/8" rabbit in the back, shape according to desires - curlycues, hooks, ogees, whatever. Put 2 on the bottom and two on the top, screw thru them with trim head screws long enough to reach the studs. Putty the tiny screw hole, paint as desired.
Or, make a long bracket for top and bottom, same width as the mirror. Not much of an artist, but the drawing should give you the idea.....