Target disk mode -big sur

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This tricks is 100% worked in my case. Just do as you said and I reboot succesfully with Big Sur OS upgraded !

Thank you very much for this detailed explanation! I was able to use Recovery Mode (Restart and hold down Command-R) to get into Terminal Mode (an option from the menus on the Recovery Mode Home Screen) and then I used my old UNIX skills to find and delete large files. The file structure was a little hard to navigate but I used the find command (find / -name Downloads) to locate where the system might have some unnecessary files. I used the cd command to change to that directory and then I used find to single out large files (find . -size +100M). I used the “rm” command to get rid of unnecessary files (reader beware of using rm unless you know what you’re doing). After that, I went up a level (cd ..) and used the find command again but this time I looked for larger files (find . -size +1G). I was able to identify a bunch of podcast videos that were 1.5-2 GB each!! Once I deleted all of those, I had a ton of free space. I restarted and the OS upgrade was successful. Thank you again for this great solution. It saved me from a total rebuild.