What appear to be the skeletons of Batman and Robin are found at Gotham City's Atomic Energy Laboratory, where the Mad Hatter left them to irradiate. Word of their demise spreads like wildfire. With the world busy mourning its loss, the Mad Hatter has no trouble snatching a valuable ruby from the Golden Buddha of Bergama's forehead. However, when rumor spreads that Batman and Robin are still alive, the Mad Hatter's scheme appears jeopardized.

The Mad Hatter has escaped from prison, and is on a quest to add Batman's cowl to his collection of hats. He attends Gotham City's annual headdress ball disguised as the Three-tailed Pasha Of Panchagorum, and snatches a large ruby off of columnist Hattie Hatfield's headdress. The villain makes a getaway, but not before turning Batman's cowl pink with a radioactive spray. He trails Batman to the Atomic Energy Laboratory, knowing he will have a chance to snatch his cowl when it is removed for decontamination.

Though Batman escapes the Sandman's trap, Robin is left to wander in a deadly maze. A clue leads Batman to Catwoman's lair, where he informs her of Sandman's plans to elope with J. Pauline Spaghetti and keep her fortunes to himself. Enraged by the Sandman's trickery, Catwoman sets out after him. Batman, with the now-rescued Robin, also follows, and the group meet up at Spaghetti's old deserted pasta factory.

Catwoman and the Sandman have teamed up, and they're after the fortunes of J. Pauline Spaghetti, a rich insomniac. Catwoman pulls a publicity stunt, getting the Sandman (under the guise of "Dr. Somnambula") an invitation to Spaghetti's penthouse - and her financial records. Batman and Robin investigate the situation, but soon find themselves trapped by the criminals.

The Puzzler continues with his plan to hijack Artemus Knab's new airplane, the Retsoor, all the while leaving puzzles behind for Batman and Robin to ponder. He familiarizes himself with the jet's designs, then prepares to fly his prize to a foreign country where he will hold it for ransom. But the Dynamic Duo have an easier time with his clues than he expected, resulting in a climactic confrontation at the airplane hanger.

The Puzzler, a villain with a fondness for both Shakespeare and aviation, indicates he is after the fortunes of Artemus Knab. He convinces the billionaire to invest in his puzzle balloon business, but when the Dynamic Duo find that Knab seems too intelligent to fall for a phony scheme, they look deeper for the criminal's true intentions. Their search leads them to Knab's airplane monopoly, but unknown to them, the Puzzler has plans to halt their investigation - permanently.

Batman and Robin escape Catwoman's trap by hitting the precise note needed to shatter the glass chamber in which they're prisoners. They quickly get on the trail of Catwoman. The feminine feline criminal eventually "steals" the voices of Chad and Jeremy, Commissioner Gordon and talk-show host Allen Stephens. She blackmails the British government, which faces the lost of revenue from the taxes on Chad and Jeremy's performances. Batman and Robin eventually capture Catwoman and her gang, but not before Batman and Catwoman express obvious affection for each other.

The Catwoman "steals" the voice of a television talk-show host in the middle of an interview with Bruce Wayne. She plants clues to suggest either the Joker, Riddler or Penguin may have committed the crime. In the meantime, she has fooled Commissioner Gordon into thinking she has gone straight. She makes her first mistake when she masquerades as Miss Klutz, a dance instructor visiting Wayne Manor. Allergic to dogwood, she sneezes and gives herself away. Her next target is to "steal" the voices of British singers Chad and Jeremy. 

Discovering why the Penguin wants to return to prison, Batman has a counterplan that needs Alfred's participation.

Facing the strange situation of the Penguin determined to be arrested, Batman must figure out why.