Catwoman
Real Name: Selina Kyle
Base: Gotham City’s East End
Special Powers and Abilities: A formidable fighter with expertise in boxing and various martial arts disciplines. She wields a bullwhip as an offensive weapon.
In-Game Abilities: Double Jump, a whip and acrobatic skills which enables her to traverse up certain walls and great distances using the acrobat poles.
Sources:
DC Comics Web Site: dccomics.com/characters
The DC Comics Encyclopedia

Robin
Real Name: Tim Drake
Base: Gotham City
Special Powers and Abilities: As the Dark Knight’s most trusted partner, Robin was trained by Batman in martial arts, as well as sleuthing skills. He is adept in the use of electronic devices, especially computers.
In-Game Abilities: Like Batman, Robin has the option to change suits with different gadgets and abilities. The Hazard Suit enables Robin to walk through toxic material, suck up and shoot toxic waste or water via the Hazard cannon attached. Robin can deploy the Zorb ball to power certain puzzles with the Acrobat Suit. He can also be immune to icy conditions with the Ice Suit and walk up shiny blue metal walls with the Magnet Suit.

Sources:
DC Comics Web Site: dccomics.com/characters
The DC Comics Encyclopedia

The Joker
Real Name: Unknown
Base: Gotham City
Special Powers and Abilities: Though not especially strong or skilled in fighting, the Joker is a dangerous villain. He often wields a deadly joke, props or gags, such as a BANG!-proclaiming flag pistol that doubles as a spear gun.
In-Game Abilities: Immunity to toxic materials or hazards. He carries a machine gun and can generate electrical power- ups using his Joker buzzer.

Sources:
DC Comics Web Site: dccomics.com/characters
The DC Comics Encyclopedia