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: