I have tried the method below on my Jiayu G2 MT6577 dual core 1GB ram version with success. Firmware version was 20120910-132127.
Download the root package from here. (Click the white button on the right) and extract it.
1. Download and install usb drivers either from Android SDK or use PdaNet drivers. New version of Android SDK installation is different from previous versions. After extracting the file, go to development/sdk/tools/ folder and run “android.bat”. Select Usb driver package to install.
2. Enable Unknown sources in Settings > Security and USB debugging in Settings > Developer options.
3. Connect your device and make sure it is recognized as Android phone (Android ADB interface) in Windows Control panel > Device manager
4. In the root package, run the RunMe.bat, type 1 and hit enter.
5. You should see messages about the process on your screen. On your phone, press ‘”restore my data” without entering a password.
6. When the process finishes, your phone will reboot. If the rooting was successful, you will see SuperSU in programs.
After running RunMe.bat, if you see error messages like “cannot create process xxx”, replace Adb.exe, AdbWinApi.dll and AdbWinUsbApi.dll files in the root package with the ones you get from your Android SDK installation folder (development/sdk/platform-tools).
Good luck!