System boots to emergency mode. How do I free up space to allow repair?

It has taken me a while but my recent crash I attribute to my root partition being full. This has probably been caused by snapper and possibly log files filling up the system but the result is that I am stuck and cannot even do a fresh installation on my root partition because of the errors which prevent the installation from proceeding.

I have tried to mount my root drive from a live DVD but this also fails and I have posted on another thread that unhappy tale.
I am sure others have been before me so please could somebody advise where I start even if it is to do a fresh install. My concerns are that that somehow my data drives may be damaged and although backed up I am talking 3TB which I would rather leave intact!
Budge

Sadly I never was able to solve this even with much kind advice from others. None worked so have deleted the partition and reinstalled.
Please consider post closed.