I was able to install Ubuntu 14.04 in my Windows 8.1 pre-installed PC. I was able to have the dual boot of the system. GRUB menu works fine, i.e. it shows both Ubuntu and Windows Boot Manager, and the corresponding OS can be booted up properly. But, if I choose Windows 8.1 to boot, and restart the PC after that, GRUB menu does not show up anymore and the PC boots directly to Windows. I found, from my BIOS setup, the boot order shows Windows Boot Manager is on the top although I changed Ubuntu on the top before. I have to put Ubuntu on the top again in order for GRUB menu to appear again. But, next time, if I go to Windows, and restart the PC, the boot order is restored back to Windows on the top and no Grub menu shows up. How can I make the boot order in BIOS does not change? I have already disabled the secure boot and fastboot, and make the system support legacy boot. But, it does not help. I guess the issue is on Windows 8.1 somehow reorders the boot order (put itself on top) once I boot into Windows 8.1.
A possible solution, is the one boot-repair uses, which is to rename the windows bootloader to a backup name, and copy in the ubuntu bootloader (grubx64.efi , unsigned, without secure boot) in place of the /EFI/Microsoft/Boot/bootmgfw.efi. Windows tends to rewrite the boot order, no fix for that. You should stay in UEFI mode to continue to boot Windows with Ubuntu.
Every machine is different, but on my Toshiba Windows will sometimes rewrite the order. I am in the habit of using a function key to invoke the EFI menu, select the HDD, then select ubuntu to boot. I have an Asus on which I cannot even keep the USB first in boot order, even without booting Windows, so things could be worse. Once you get the fake bootmgfw.efi in place, things should be stable for you.