In Batman: Arkham City for the PS3 and Xbox 360, the game is based on checkpoints and automatic saves. There is not a built in way to save your game via the menus, but there is a work-around for this.
The easiest way to force the game to save is by simply entering or exiting a building. There are a lot of buildings in the city you can enter, so just turn on detective mode and look for the nearest glowing door.
Alternatively, the game will also save after you beat up a group of bad guys.
