This is Spicy Mystery Stories for February 1936, cover by H.J. Ward. The ISFDB entry for this issue is here. This image of the cover is an unusually large one (click through to see in larger size), which I found in, of all places, the comments section of this post at Door Flies Open.
In additional all the other unusual riches available for this issue, Pulp Covers has actually made available the “Bat Man” story online as a PDF document, in case you’re curious about what lurked beneath the lurid covers of a pulp magazine. See here.
Maybe he’s one of the Batman’s mates?
( https://eroticmadscience.com/2017/03/25/pulp-parade-43-weird-wedding/ )
Interesting possibility. When tweeting the image just now I advanced this conjecture:
Well, he does let the villain die in his very first story.