Your BIOS setup may look different from this, but this is what mine looks like when it works the way I want (dual boot via Grub):
|My BIOS "Boot" Configuration|
|Dell file chooser|
Under <linuxmint> you should see this:
The grubx64.efi file is the one you want, this one will start Grub on boot. Once you've selected this file, you will probably be asked to name the new boot configuration. You can call it whatever you want. Once you've given it a name (I called it "mint"), you will want to make it the first boot priority as in the first photo of this article.
Another problem I ran into once (again after a Windows 8 'update') was messed up partition flags. Here is what my "working" partitions look like:
I've highlighted the partition flags at right. You will of course need to know what you're doing if you start messing with these. The important flags are "boot", which is on /dev/sda1 here, and the "msftres" flag which is on an 'unknown' chunk of the disk. Make sure these are set properly.
Finally, when things really go wrong and you can't boot into Windows 8 anymore, you may need a Windows 8 rescue image. This can be generated from a working copy of Windows -- even a working copy from a friend that has Windows 8. If you can't find a friend that has it, maybe you can go to a local computer store and get one made... You just need an 8GB USB memory stick. I had to borrow one one from a friend of mine in order to use the utility called "bootrec". The general procedure was something like:
- Boot Windows 8 recovery from USB drive.
- Get to a command prompt and run the following:
- bootrec /fixmbr
- bootrec /fixboot
- bootrec /rebuildbcd
So that's it. For any problem you may have, I think you've got the information here to solve it.