After reading my post about Signet’s various Batman tie-ins, Jeff recalled that he had two of the paperbacks, scanned the covers and sent them to me. The books Jeff has are Batman vs. 3 Villains of Doom, the one actual tie-in novel, and Batman vs. The Penguin, the third collection of reprints from various Batman comic books. According to the back cover of Batman vs. 3 Villains of Doom, the story involves the Penguin, the Joker and Catwoman vying for “the coveted TOMMY–the crimeworld’s top award.” All the winner has to do is “outwit or destroy” Batman and Robin.
Here’s the cover to Batman vs. 3 Villains of Doom:


And here’s the cover to Batman vs. The Penguin:


BATMAN vs THE 3 VILLIANS OF DOOM was really a pretty good read. I remember that some plot points were taken from late 1950s Batman comic stories. I still have my copy, purchased in 1966.