It seems like the problem may be more than just the update not going through. I've tried sfc /scannow and that doesn't seem to work either. I have no idea where the root of the problem lies.
I see the following errors reoccuring in the systems event logs
The application-specific permission...
https://www.microsoft.com/en-us/download/details.aspx?id=48145 this is where i got it from... and i've seen users who had successfully installed it.
https://www.reddit.com/r/DolphinEmulator/comments/3jsiph/as_of_407538_dolphin_now_requires_visual_c/
----UPDATE
I tried DISM.exe /Online...
I am on windows 8.1 pro and I'm trying to install Microsoft Visual C++ 2015 Redistributable (x64) 14.0.23026
I am also having issues with some updates as well which I know is related.
Anyways, the 0x800f0830- Unspec error, has a log file and this is what it says...