Batman: Arkham Unleashed is the sequel to Batman: Arkham City. It takes place a year after the events in Arkham City, and all of Batman's enemies escape Arkham Asylum into Gotham City.
Riddle 1: "This person ended up in here, kind of a big JOKE, don't you think?" - Go to the Ace Chemicals Processing Plant and scan the vat of chemicals with a graffiti message saying "The Start of the Joke".
Riddle 2: "This is where the first BOY WONDER started and how the NIGHT dawned over Gotham's WING" - Go to the Batcave and scan in the Robin and Nightwing costumes together.
Riddle 3: "You don't have to give yourself the COLD shoulder" - Go to the Gotham City Police Station and go to the evidence room and scan Mister Freeze's weapon.
Riddle 4: "This MAN was inspired by the BATman" - Go to Man-Bat's lair underneath the Arkham City memorial and scan the papers and designs.