How to fix Windows Backup Error Code 0x8078015B
Solution 1:
Are you backing up any remote shares?
This "0x8078015B - Error when accessing the remote shared folder [archive.org]" seems to be the only thing I can find with that error code along with a solution.
If you're getting the errors below while doing a backup in Windows 7, just delete or move your old backup. For some reason, to do a 500+ GB backup, it needs 500 GB free in addition to the space it's about to delete from the previous system image. I guess they do it by creating the full backup first and then deleting the old one. So if you want to keep 500GB backed up, you'll need 1TB of space (plus the normal 10% margin for error, so 1.1TB).
And of course Windows won't let you choose to include a system image of only one drive... grrr, the one Windows is on is the only one that needs an image; the rest is backed up elsewise... but whatever. Just wipe your old one and it'll finish fine.
Hope it's of some use.
Solution 2:
I went through the same problem, but found the answer today. Go manual, pick the harddrive you want to save on, then when you reach the list of the file with the checkbox, outside the the central square of the window there's another checkbox. Uncheck it and it should work, that's what it did for me.