Yesterday I was trying to upgrade a VM to Windows 8.1. The VM had Windows 8 on it.
The host software I used was Hyper-V from Windows 8.1 Preview
By itself the VM worked fine, and I was able to install the package that allowed me to download the Windows 8.1 Preview from the store and install it through there.
However upon completion of the download and the subsequent reboot I was greeted with the following error:

0x800705AA – 0x2000C
The full error is
Couldn’t update to Windows 8.1 Preview
Sorry we couldn’t complete the update to Windows 8.1 Preview. We’ve restored your previous version of Windows to this pc.
0x800705AA – 0x2000C
And the upgrade didn’t happen.
Googling on error 0x800705AA – 0x2000C didn’t help a lot. So I decided to investigate: I found out that I had set the Startup RAM of the machine too low. Because it had dynamic memory it wasn’t an issue WHILE running Windows 8, but it seems that during the installation of 8.1 something goes wrong and the VM thinks it doesn’t have enough RAM, hence the error.
So by setting the RAM of the machine to, say 2GB I managed to mitigate the problem. After that the upgrade went like a charm.

Have a good one,
-Kristof