The Arkhamverse is one of the many infinite universes in the Omniverse that is seen in the Batman Arkham games and tie-in comics
The Arkhamverse is a universe that centers around Batman, it is unknown if the other DC heroes populate the universe, though the cities of Metropolis, Star City, Coast City, etc. have been shown to exist in the Arkhamverse as seen on billboards or mentioned by the inhabitants.
The Arkhamverse has no established date when it's stories take place, this is all based on speculation.
1985: Bruce Wayne is born to Thomas and Martha Wayne.
1993:Bruce Wayne witnesses the murder of his parents in Crime Alley to an unnamed gunman who is never brought to justice.
1999:Bruce Wayne at age 14 travels overseas to train to become Batman.
Mid-2000's: Bruce Wayne learns Martial arts in Korea.
Late 2000's:Bruce Wayne returns to Gotham after training overseas to become a crime fighter.
2009:Bruce Wayne becomes the Batman.
The Red Hood begins his crime-spree.
Batman and the Red Hood encounter each other at the ACE Chemicals Plant, following the scuffle, the Red Hood falls into a vat of chemicals, turning him into the Joker.
December 24-25: The events of Batman: Arkham Origins
December 31: The events of Batman: Cold, Cold Heart
Batman meets Catwoman.
The events of Batman: Arkham Origins: Blackgate.
Batman: Assault on Arkham animated movie.
Batman: Arkham Asylum
Arkham City opens.
Batman: Arkham City.
Harley Quinn's revenge dlc.
Batman: Arkham Knight
End of the Arkhamverse