Have you tried Using SFC (System File Checker) and DISM (Deployment Imaging Servicing and Management) to Repair Windows 8 & 10?
When things have gotten really ugly that's step one (which I should have suggested before). The second is to try the ISO update method. After that I tend to go one of the "thermonuclear" routes after having taken a full system image backup using the utility of your choice along with a separate user data backup as well.
1. Reset with "Keep My Files" (knowing that most of the Desktop Apps and Store Apps you've installed will disappear in the process).
2. Reset without keeping files.
If either of the above work you can try updating again.
If you wish to avoid even dealing with a Reset then back up your user data, back up your full system image, use something like Belarc Advisor to get a list of what you have installed on the computer (as I always forget something and it's simple and free to use this tool to get a software inventory on your system), then do a clean install of Windows 10 using an ISO that was created after whatever is the latest version (right now: 1709) was released.
Someone else may have a better idea and I'd certainly love knowing how to avoid resets and/or clean installs.
But, I emphasize again, in order to give any sort of accurate guidance more information regarding exactly why the install is failing is needed. All of the above is offered with the proviso that it is "my general approach" but that may not be appropriate for certain quirky failures.
Brian AKA Bri the Tech Guy (website in my user profile) - Windows 10 Home, 64-Bit, Version 1803, Build 17134
Memory is a crazy woman that hoards rags and throws away food.
~ Austin O'Malley