Not much is known of Earth-One's Cluemaster, aside from the fact that he displays remarkable ingenuity and a tenacity towards his goal... discovering Batman's identity!
To that end, he created his costumed persona, used several topsy-turvy clues to draw his foe out, then have his hoods track the Masked Manhhunter. When confronted by Batman, he used several trick pellets he wore such ones that release smoke, gas and explosives.
Mister Baffle was a jewel thief who came to Earth-Two's Gotham City relishing the thought of matching wits with Batman, while preying upon his foe's alter ego millionaire Bruce Wayne. When he realized that he was getting nowhere against his costumed foe, he promptly left Gotham never to return. A man with his name using gadgets later appeared to duel with Robotman in 1949... could this have been the same man changing his modus operandi?
Back to Cluemaster, the criminal would reappear three more times alongside fellow villains in Gotham City yet found no further success against the Bat.