Murad IV of the Ottoman Empire supposedly wandered the streets of Constantinople in disguise at night, in search of people breaking his coffee and alcohol ban, and murdered them personally.Your challenge is to have a prominent medieval nobleman moonlight as a crusader for law and justice using an alias, helping the poor and protecting people from villains and so forth. He has to have all of Batman's accoutrements: high tech equipment for his time, strong armor, disguise, secret lair, and so forth. Needless to say, he has to be very wealthy to develop all of this tech. He will never kill, just like the character.
His identity is kept secret: presumably he does something to make sure it doesn't leak out. You can probably assume he's doing this with the permission of the local lord (if he is not that person himself). He can have associates as well (like OTL Robin) whose identities are also kept secret, but the fewer associates the less chance of a breach.
Politically, this man could favor the aristocrats as a nobleman but make sure that poor get their fair share by protecting them using his alter ego. You don't want the other aristocrats to realize you're preventing them from oppressing their peasants.
The most obvious example is a young Leonardo da Vinci. Can he do it based on the inventions he's made? Anyone else?
I guess he's more of a... Red Hood than a Batman though, lol.