All good :) Happy to try and help.
Disclaimer: this was all new to me as well. I was simply following some steps seen online, so approach this at your own risk. It was a last resort for me, so don't go on from here unless you feel it's worth the risk.
Here's the main forum I referenced when looking into this - https://apple.stackexchange.com/questions/197503/how-can-i-delete-files-in-recovery-mode-using-terminal-on-my-os-x-main-partition.
To start, head back into Recovery Mode. Under the Utilities menu, you'll find Terminal.
I'm assuming you have verified that a lack of storage was likely the issue by following the steps I mentioned previously, so your goal now is to locate something on your drive of sufficient size to delete and free up space for the update to complete.
Start easy. Type in cd /Volumes then ls to list all mounted volumes. Hit enter after each command. You should see something like Macintosh HD and Macintosh HD - Data listed, and possibly others. Macintosh HD - Data is typically where your files are located.
If you're not familiar with exactly how the directories are set up, you can use the ls command again to look around. For example, if you want to see all the Users on your drive, type in cd "Macintosh HD - Data/Users/" followed by ls to see a list of the Users. You can then use the same pattern to slowly move through your folders and find something to delete.
A couple of tips if you run into trouble:
- Make sure to have the opening and closing " with each command. Without this, the spaces in the volume names will screw it up and the command won't be recognized.
- Also, try the long-form commands in full and test things with and without a / and the beginning and end of the commands. I can't recall the exact pattern that eventually worked for me but I know I messed with this a bit before I figured out what I was missing. When I say long-form, I mean without the shortcuts - in case you try a command that doesn't work along the way. For example, always include /Volumes/Macintosh HD - Data/ when going deeper into the directories, even if it may not be necessary each time.
So you might try commands like cd "/Volumes/Macintosh HD - Data/Users/<username>/" and cd "/Volumes/Macintosh HD - Data/Users/<username>/Downloads/" where <username> should be replaced with your Mac username. If unsure of your exact username, use the command I mentioned earlier to see a list of Users.
Up to this point you're simply navigating around your drive - much like you would in Finder - the only difference being you're typing it all in and not using a nice UI.
From here, it's important to make sure you're in the right directory because the commands get more serious when you start deleting things. I can't stress this enough - only delete things you are 100% sure are safe to be deleted. This is a permanent deletion - there is no Trash to recover it from later. If anything looks remotely like a necessary system file, stay clear of it. I do not know what the ramifications could be if you delete something important. You shouldn't really come across anything like that if you're in the place of Downloads, Documents, Photos, etc. but it goes without saying to be extra careful. If you don't feel comfortable deleting things, I'd suggest finding a professional to help.
If you believe you are in the right directory (use the ls command as much as you want to make sure) then you can move to delete something using the rm -r or rm -rf command (see forum link for the differences between the two).
For me, I knew I had a large (10GB+) zip file of Photos that I had neglected to delete in my Downloads folder so I used cd "/Volumes/Macintosh HD - Data/Users/<username>/Downloads/" and then listed everything in it using the ls command. I scanned the list it gave me, looking for the name of the zip file - Photos. I found it so knew I was in the right place. Without leaving the Downloads directory, I typed in rm -rf Photos and hit enter. And away it went.
It may look like it didn't do anything - if I recall correctly, the Terminal sort of briefly flashed to indicate something happened. The best thing to do is use the ls command again to give a list of the directory in its current state and see if the file or folder you chose to delete is now gone. Repeat this until you feel like you've freed up enough space to complete the update. It's impossible for me to say how much you need to delete, I would just suggest you rid of as much as you can safely. I suspect my 10GB+ file was more than enough and you probably don't need that much but it's impossible to say.
Once you feel good about it, it's time to let the update try its thing again. For me, it was as simple as exiting Terminal and restarting the Mac under the Apple menu. It cycled back to the 29-minute countdown like it always had been but this time it kept going all the way through to a successful completion and reboot.