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.

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.