Yeah I was trying to upgrade to Sierra but then I got an error. It said "file system verify or repair failed".That should give you terminal, which gives you access to disk utility from the menu.
You mention an OS installation. I don't know if that means upgrade, or fresh install.
But with disk utility you can run first aid to repair the boot stuff (it should do that for you)
and you can probably partition your disk there.
NOTE: partitioning and formatting makes you LOSE ALL YOUR DATA ..
Who knows though, if you can get into recovery mode, with cmd+r you can perhaps access the data and find a way to back it up. Maybe it's super easy, I dont know, mac usually dont fail on me so dont have too much experience with it. But since the terminal is there and unix under the hood, i dont know why it wouldn't let you mount a volume and external volume and cp (copy) data over.
Just not sure what your game-plan is with the os installation.
I ran the first aid again with the error and took a picture.0 = no errors, 8 isn't good.
Maybe try something like this? http://osxdaily.com/2013/08/07/how-to-repair-a-mac-disk-with-fsck-from-single-user-mode/
What I read on this forum though is people reporting exit 8 on external drives? Maybe unplug any external usb devices you dont need for an upgrade. Reboot, and try again?