On an urgent call from Commissioner Gordon, Bruce Wayne and Dick Grayson switch to Batman and Robin and rush to The Gotham Plaza Hotel; once there, they are surprised by a party being held in celebration of Batman and Robin's anniversary of their partnership with The Gotham City Police Department. During the presentation of a golden calf filled with $200,000 intended for charity, the party is interrupted by erupting clouds of green smoke and the sudden appearance of three emergency firemen who swipe the calf and escape through an open window. Before making his escape, one of the firemen reveals himself to be that crooked Count Of Conundrums himself, The Riddler, in disguise, who drops off one of his criminal clues, and then drops out to a safety net placed just outside! The Dynamic Duo attempt to give chase in The Batmobile, but lose the getaway truck in some Riddler-planned confusion. Following up on Riddler's clue, The Dynamic Duo analyze a crossword puzzle in The Gotham Herald newspaper. Believing they have solved the puzzle, and that it holds the key to The Riddler's next caper, they put through a call to Gordon by Batphone to alert him. However, Gordon informs them that the underground vault of The Gotham City Bank has been flooded (obviously engineered by Riddler and crew!).

Realizing they have misread the clues, Batman and Robin track Riddler to the bank where he and his henchmen Across and Down (in frogman wetsuits) are attempting to steal the cash. Armed with Batrespirators, The Duo give battle; during the fight, Riddler yanks off Robin's respirator and tosses it asunder, causing Batman to rush to his aid and give Riddler and his minions the distraction they need to split. The trio of supercrooks reconvene at their hideout at the soon-to-be-opened Norman Jigsaw Puzzle Factory, where they meet up with their moll, Anna Gram (oh, brother!) and to dry out the stolen money, for The Prince Of Puzzlers wants to collect $3 million in order to bargain for a horrifying weapon from Professor Avery Evans Charm: a pen-sized Demolecularizer. Meanwhile, Batman and Robin remember their appointment with The Gotham City's Bakers Guild to pose for lifesize marshmallow figurines, which will top a giant cake. Unknown to them, The Riddler, Across and Down have replaced the guild members! They lift The Caped Crusader and The Boy Wonder by forklift to the top of the 3-story cake; then, with a click of a switch by Riddler, Batman and Robin find themselves stuck as the cake directly under our heroes is made of 15 feet of lethal quicksand cleverly disguised as strawberry icing! As The Dynamic Duo slowly sink to oblivion, The Riddler and his men depart to prepare his next criminal scheme.