Installation error: upgrade from Sierra to High Sierra

Have you tried resetting your mini's SMC or used Apple Diagnostics yet?

• How to reset the System Management Controller (SMC) on your Mac - Apple Support
• How to use Apple Diagnostics on your Mac - Apple Support

I suspect that, like HWTech, that your mini's internal drive may be corrupted or failing. I again suggest that you boot up your Mac in Recovery Mode, and then, use the First Aid option in the Disk Utility to see if any errors are reported. Should you not be able to enter this mode could mean that the Recovery partition is either missing or corrupted. In that case you would need to boot up your mini in Single-User mode. Then enter the following in the command prompt that will be displayed:

/sbin/fsck -fy <enter>

Let it run and see if any errors are reported.

I suggest that you boot up your mini in Safe Mode, and then, try running the installer again.

Ref: Use safe mode to isolate issues with your Mac - Apple Support

The next option would be to create a new user account. Log out of your existing account, and then, log back in with the new account. Try running the installer again. If it still fails, it may be possible that your mini's drive may be damaged. If that may be the case, try using Disk Utility's First Aid process to detect and repair it.

You should check the health of the hard drive. You can do this using DriveDX. If there are any "Failures" or "Warnings" it means the drive is either failing or worn out respectively. If you are unsure or if you have an SSD, then post the report here using the "Additional Text" icon which looks like a piece of paper.