"Batman: Arkham Trilogy" gets a confirmed release date of October 13th for Nintendo Switch
The trilogy seems to be exclusive to the Nintendo Switch, as a specific article on Warner Bros. Games' website about the trilogy package has a short FAQ, in which they specifically mention that "Batman: Arkham Trilogy is only scheduled to release on Nintendo Switch". However, only 3 out of the 4 Arkham games, excluding Batman: Arkham Origins from what could-have-been a collection of the whole series, and this could have been due to the fact that said game was instead developed by Warner Bros. Games Montreal while Rocksteady Studios were working on Arkham Knight.
The trilogy will consist of Batman: Arkham Asylum, Batman: Arkham City and Batman: Arkham Knight, with each and every game in the package having all the previously released DLC included into their respective games.
As usual with most collections or packages of franchises released for the Nintendo Switch, only the very first game (Arkham Asylum) will be included in the cartridge, while both Arkham City and Arkham Knight will require an online connection to download and install said games into the Switch.
Batman: Arkham Trilogy page on Warner Bros. Games