Classic Batman
Classic Batman-billionaire Bruce Wayne lost his parents to a mugging leaving him alone and in need of vengeance, he spent his life training to one day become a symbol to protect Gotham, a symbol known as Batman, his first appearance is in detective comics #27
Batman Beyond
Batman beyond-Batman beyond is the batman of the future, alter ego terry mcginues stumbles into the bat a e and steals the batsuit, eventually with the help of an older Bruce Wayne is the protector of Gotham city, his first appearance was in Batman beyond episode 1 rebirth
Red Son Batman
Red son Batman-this version of Batman became a ruthless anarchist after his parents were gunned down by Stalin's police force, vowed revenge on Pyotr Roslov and 20 years later, became the most wanted man in the Soviet Union. His first appearance was in Superman:Red Son #1
Flashpoint Batman
Flashpoint Batman-(real name Thomas Wayne) is a ruthless and exasperated vigilante in the Flashpoint timeline. Driven to vengeance by the death of his son at the hands of a mugger, he now slaughters criminals across the multiverse, trying to erase his world and restore his son to life.his first appearance was in flashpoint volume 2 #1
The Batman Who Laughs
The Batman who laughs is a "Jokerized" evil version of Batman who originated from the Dark Multiverse. After killing the joker in an altercation he had breathed in a special version of joker venom slowly driving him insane. His first appearance is in Dark Days:The casting #1
Blackest Night Batman
Blackest night Batman- is a clone of Bruce Wayne created by darkseid to convince earths heroes that Batman was dead, and was later revived the the power of the black lantern ring to recruit more long dead heroes the the cause, his first appearance was in green lantern volume 4 #43
Injustice Batman
Injustice Batman- was a version Batman who fought against Superman’s regime in the injustice gods among us video game and is the only member of the Justice league to side against Superman. His first appearance was in the video game injustice gods among us by netherrealm studios
Arkham Batman
Arkham Batman is a version of Batman that was trapped within Arkham asylum leading to a series of events fighting many different villains in many different versions of Arkham asylum that followed, that behind Arkham city and eventually leading to a confrontation with scarecrow that revealed his identity forcing Batman to go under ground and fake his death. His first appearance was in Batman Arkham asylum the video game by rocksteady.