https://store.steampowered.com/app/200260/Batman_Arkham_City__Game_of_the_Year_Edition/

Batman: Arkham City builds upon the intense, atmospheric foundation of Batman: Arkham Asylum, sending players flying through the expansive Arkham City - five times larger than the game world in Batman: Arkham Asylum - the new maximum security "home" for all of Gotham City's thugs, gangsters and insane criminal masterminds. Featuring an incredible Rogues Gallery of Gotham City's most dangerous criminals including Catwoman, The Joker, The Riddler, Two-Face, Harley Quinn, The Penguin, Mr. Freeze and many others, the game allows players to genuinely experience what it feels like to be The Dark Knight delivering justice on the streets of Gotham City.

Batman: Arkham City - Game of the Year Edition includes the following DLC:

Catwoman Pack
Nightwing Bundle Pack
Robin Bundle Pack
Harley Quinn’s Revenge
Challenge Map Pack
Arkham City Skins Pack

Batman: Arkham City - Game of the Year Edition packages new gameplay content, seven maps, three playable characters, and 12 skins beyond the original retail release:

Maps: Wayne Manor, Main Hall, Freight Train, Black Mask, The Joker's Carnival, Iceberg Long, and Batcave
Playable Characters: Catwoman, Robin and Nightwing
Skins: 1970s Batsuit, Year One Batman, The Dark Knight Returns, Earth One Batman, Batman Beyond Batman, Animated Batman, Sinestro Corps Batman, Long Halloween Catwoman, Animated Catwoman, Animated Robin, Red Robin and Animated Nightwing

Activating the steam key

1) You must download and install Steam http://steampowered.com/download/SteamInstall.msi (if not already installed).
2) Create a new account on Steam or go to an existing one.
3) Select "Activate via Steam ..." in the "My Games" section, and enter the key received after payment.
4) After activation, the game will appear in your list of games and you can install it.

Please leave feedback after successful activation of the game.