Detective Comics #192

A criminal known as the Phantom Eye of Gotham begins to televise crimes as they happen and makes the Dynamic Duo look like they are inept. He goes further to disguise himself as Batman and get unmasked on TV as a wealthy big-game hunter, Byron King, forcing Batman to investigate who is behind the Phantom Eye broadcasts and discover why King would be masquerading as Batman.

To make things worse, the criminal manages to get footage from the Batcave and Batman decides that it's time to do some investigation as Bruce Wayne. Using his connections among wealthy Gothamites, Bruce learns that the Byron King is really an impostor that has been holding King and his son prisoner. After following the criminal to his secret island sanctuary, Batman learns all the details of the criminal scheme to use the Phantom Eye's broadcasts and King's perceived masquerade as Batman to occupy Batman while the real crime of stealing King's fortune was taking place. With the real crime and the real King's location revealed Batman emerges from hiding and captures the criminal before the plot is complete.