Usual disclaimers apply but this is the method I used successfully on a Nokia Lumia 710
and an LG Quantum:
After downloading the App (see bottom of page) and running you will be presented with the following dialog:
Click ‘Install WP7.8
I then got the following dialog and selected OK:
This took me to this URL which proceeded to download the tools.
I opened the download using WinRar:
There are two executables, one for 32bit and one for 64 bit.
I ran the 64 Bit version called “Setup-UpdateWP-x64.exe” which ran quite quickly.
I then returned to the first screen and tried again:
I was prompted to select a language:
I selected ‘English (United Kingdom’): and the update proceeded:
My device buzzed and I got the ‘do not unplug’ logo while the animated graphic (above) continued for around 10 minutes, at which time my phone rebooted and reported a sucesfull update. Checking the version under settings->about on the phone showed that I was now on version 7.10.8779.8
I repeated the above process, SevenEighter then proceeded to download, then transfer the updates.
When done my phone showed the ‘do not disconnect’ logo and the process continued as previously. After 5 minutes the phone rebooted. This time it reported the version as being 7.10.8783.12
I repeated the cycle again and this time got 7.8!