Upgrading to windows 8.1 on a dual-boot computer

I need to upgrade to windows 8.1 (from Windows 8), but when I use the windows store to upgrade I get error "application wasn't installed", and error code 80070002.

I am dual-booting with Linux (Debian stable), using default GRUB bootloader, but have marked the windows partition as "Active" as per the advice at Windows 8.1 install error 0x80070002. (also as per there, I tried clearing the windows store cache and deleting C:\Windows\SoftwareDistribution\Download)

According to disk management, my primary hard drive has

• 350 MB NTFS system reserved (Healthy, system, primary partition)
• C: 92.53 GB NTFS (Healthy, Boot, Page file, active, crash dump, primary partition)
• 25.52 GB (this is primary linux partition)
• 862 MB (my linux swap partition)

And I wonder if this unconventional partition structure might be the problem (I don't actually know that the first 350 MB partition is).

Otherwise, I'm totally out of ideas. Any ideas what the problem might be?

EDIT ANSWERED: See comments: Thanks to magicandre1981 for "disable grub, use win bootloader to update to 8.1, install all updates, enable GRUB again."