When he resolved to dedicate his life to an endless war on crime, Batman declared that criminals are a "superstitious, cowardly lot," vowing to use their fear against them. To that end, he crafted his crime-fighting persona into a horrifying creature of the night, appearing from the shadows to brutalize those who would harm the innocent. While he's just a man in a costume, Bruce Wayne persuaded the criminals of Gotham City to see him as their personal demon - a form he literally took on during one adventure with the Justice League.
In JLA's 'Golden Perfect' arc, Wonder Woman loses faith in her iconic Lasso of Truth. Because she's the divine guardian of truth as a metaphysical concept, this moment of doubt causes a chain reaction through magic which begins to eat away at the objective truths underlying reality. As this process worsens, reality is warped more and more by shared beliefs - the world is suddenly square, the moon is made of green cheese, various gods manifest on Earth, and the Justice League of America take on new forms based on how people see them.
In JLA #64 (by Joe Kelly, Doug Mahnke, Tom Nguyen, David Baron, and Ken Lopez), the team arrive to help Wonder Woman defeat the villain who caused her initial doubt in Truth. Unfortunately, they've already become their perception-based selves, limiting their effectiveness. Superman has become a caricatured living god, Plastic Man is reduced to literal comic relief, newbie Green Lantern Kyle Rayner is slowly transforming into his famous predecessor Hal Jordan, Flash's powers are going haywire, and Batman has become a demonic creature of the night.
What's worse is that Batman's demon form isn't stable. While many see him as a horrific supernatural creature, others believe that he's an urban legend that doesn't actually exist, and he's gradually fading from reality as objective truth degrades. Bruce has built his entire persona on the fear and uncertainty of criminals, but when he's forced to live as the creature they imagine, there are major consequences. Ironically, the member of the Justice League with no powers is the one who becomes least human, showing just how essential Batman's reputation is to his crime-fighting efforts.
Batman's reputation is well-earned, but it's also a carefully curated weapon in his arsenal. A genius who has trained to the limits of human ability, Bruce Wayne is nonetheless flesh and blood, and he creates every advantage he can to stay two steps ahead of his enemies and one step ahead of his allies. In this case, however, the persona of terror he's created backfires, representing a figure of terror so unbelievable, a significant number of people are sensible enough to know he couldn't possibly exist.
Given years of continuity and his various world-saving feats, current comics tend not to draw on the idea that the world doesn't know who or what Batman really is, or even if he's real. However, this fascinating look into that perspective showed just how effective Bruce has been in turning himself into a supernatural terror. Especially in a world of genuine superhumans, it helps contextualize Batman's success to understand that this formless, shadowy demon is what criminals believe is hunting them as they stalk the streets of Gotham.