Over at GeForce.com you will find the system requirements you will need to rescue Gotham from its current status of Arkham City.  They are fairly modest to be able to play the game at a reasonable resolution, if you are willing to skip out on PhysX, 3D Vision and extreme tesellation.

In concert with a 2.4GHz Dual-Core CPU and 2GB of RAM, a GeForce 8800 GT will give you a high level of visual fidelity, but none of the extras. A GeForce GTX 460, however, in conjunction with a 2.5GHz Dual-Core CPU and 4GB of RAM, will allow you to use the game’s Recommended ‘High’ settings and PhysX, as shown in our recent Batman: Arkham City PC Trailer.

Based on preliminary testing we’ve determined that a GeForce GTX 460 or GeForce GTX 560 will allow you to play Arkham City comfortably at 1920×1080 with PhysX enabled, as shown in the aforementioned video; a GeForce GTX 570 allows you to enable additional DirectX 11 effects, as shown in our screenshot; and a GeForce GTX 580 allows you view all of the eye-candy in stereoscopic 3D Vision for the ultimate Batman: Arkham City experience.

Minimum System Requirements

    Operating System: Microsoft Windows XP, Vista or 7
    CPU: Dual-Core CPU 2.4 Ghz
    RAM: 2GB
    Graphics Card: NVIDIA 8800 or ATI 3800 with 512MB of VRAM
    Sound: Microsoft Windows XP/Vista or 7 compatible sound card (100% DirectX 9.0c-compatible)
    DVD-ROM: Quad-speed (4x) DVD-ROM drive
    Hard Drive: 17.5GB free disk space
    Input Devices: 100% Windows XP/Vista or 7 compatible mouse and keyboard

Recommended System Requirements

    Operating System: Microsoft Windows 7
    CPU: Dual-Core CPU 2.5 GHz
    RAM: 4GB
    Graphics Card: NVIDIA GeForce GTX 460 or ATI Radeon HD 6850 with 768MB+ of VRAM (DirectX 11 compatible)
    Sound: Microsoft Windows XP/Vista or 7 compatible sound card (100% DirectX 9.0c-compatible)
    DVD-ROM: Quad-speed (4x) DVD-ROM drive
    Hard Drive: 17.5 GB free disk space
    Input Devices: 100% Windows XP/Vista or 7 compatible mouse and keyboard or Xbox 360 Controller for Windows