Batman™ and all related elements are property of DC Comics, Inc. There were 2 versions of this game released - the most obvious difference being the title screen.
There are numerous other games called Batman Returns which appear on other systems (e.g. DOS, Game Gear, Lynx, Master System, Megadrive, Mega CD, NES, and SNES), however they are very different in design to the Amiga version.
UK Advert (CU Amiga 10/1993, Page 12)
French Advert
Manual (English/French/German)
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Gotham Christmas
Gotham Mayhem
Gotham Rooftops
Train
Sewer
Penguin's Hideout