Batman prevents a radium robbery at Gotham Hospital. During his fight with the crooks, Batman is shot in the knee. The bullet shatters his kneecap. Batman then leaves and returns as Bruce Wayne, claiming to have been wounded while cleaning a gun.
During his stay at the hospital, Batman learns that the radium was actually stolen, though not by the gunmen. Despite his injury, Batman investigates, finds the missing radium, and the thief. Nurse Noreen O'Day suspects Bruce is Batman, but he throws her off by changing the pattern of his heart beat to throw off her test.
[1] plot summary at dcindexes.com
While Batman is in Hollywood shooting an anti-crime movie, crooks steal the film cannister containing a new movie produced by the studio. The crooks try to blackmail the studio for the film. Batman plans a trap for the crooks, but it fails. However, he does recover the film. Learning it is a flop, Batman suspects the director was involved in the theft. He gains proof against the director, then apprehends him along with his hired thieves.[2] plot summary at dcindexes.com
After escaping from jail, the Joker creates his own versions of Batman's equipment including: a Jokermobile, Joker Signal, and Jokergyro helicopter. Joker then sells his services to crooks, who use the Joker Signal to summon him when then run into problems.
After a failed attempt to stop the Joker, Batman uses several Joker Signals to lure the crook out of hiding. Then he follows him back to his hide-out. However, Joker beats Batman and steals the Batmobile. Batman escapes a trap, then uses the Jokermobile to hunt down and capture the Joker, returning him to prison.
[3] plot summary at dcindexes.com