I ran into this problem myself when I was setting up my new Ivy Bridge system tonight. Was the first time I tested the HD6870 in ML, worked fine in Lion in the past. The solution was actually not an obvious one as suggested by some of the responders here - but I did work one out which I will discribe briefly.
Basically, force VESA mode by simply removing the ATI6000Controller.kext from the myHack OS X Install Disk. I would suggest doing it as follows:
In a terminal with the OS X 10.8 myHack OS X Install Disk connected to the system run the following:
sudo mv /Volumes/myHack\ OS\ X\ Install\ Disk/System/Library/Extensions/ATI6000Controller.kext /Volumes/myHack\ OS\ X\ Install\ Disk/Extra/RemovedExtensions/
Then run myfix on the myHack OS X Install Disk via the myHack application or terminal.
Now boot the myHack OS X Install Disk on the system you were having issues with, use the following Chameleon boot flags:
GraphicsEnabler=No -v
You will now get to a GUI, with limited and ugly resolution - but it will function. - Don't worry, the HD6870 actually works great in ML itself, this is only an issue with the ML Installer.
After installing ML, boot the system to it. You will once again have to boot with the GraphicsEnabler=No -v boot flag.
After you get through the initial setup, account creation, etc and login - pop open a terminal and reverse the process you did before.
Make sure the myHack OS X Install Disk is attached to the system and run the following command:
sudo mv /Volumes/myHack\ OS\ X\ Install\ Disk/Extra/RemovedExtensions/ATI6000Controller.kext /System/Library/Extensions/
This will put the extension back in it's place. Then run myfix again - this time targeting /
Once completed, reboot the system - Use GraphicsEnabler=Yes (this is the default value in myhack org.chameleon.Boot.plist so you will not have to type it unless you modified the value in the plist) and enjoy your fully functional HD6870 in ML.
Cheers.