How do you install Linux alongside Windows 8 without corrupting the Windows 8 boot configuration?

It's tricky to switch between BIOS-mode and EFI-mode OSes on a single computer; for best results, you should keep both OSes in one boot mode. Your best bet is to install an EFI-mode boot loader for Mint. Several are available, but installation can be tricky. Specific options you might want to try include the following:

• Use Ubuntu's "Boot Repair" tool (I think it's part of the Ubuntu installer), which may set things up correctly for you, and with minimal fuss. I can't make any promises of this, though, since you're using Mint. Also, the Boot Repair tool can set things up in a rather unusual way that can cause confusion for other utilities down the road.
• Boot a Linux emergency system in EFI mode and manually install an EFI boot loader. I describe several here, as well as manual EFI boot loader installation. Mint uses GRUB 2 in EFI mode, but a manual installation will take more effort to integrate with Mint's package. ELILO is easy to set up and use by manual standards, but it will require maintenance every time you upgrade your kernel. rEFInd is easy in terms of ongoing maintenance, but its installation script might not work well from an emergency system.
• Install rEFInd in Windows (as described in its documentation), along with an EFI driver for whatever filesystem you used for Mint (on its root partition or /boot, if you've got a separate /boot partition). When you reboot, rEFInd should come up and give you options for Windows and Linux. Select one of the Linux options, press F2 or Insert twice, and add ro root=/dev/sda7 to the boot options, changing /dev/sda7 to your Mint root (/) partition. When you press Enter, Mint should start up. When it does, run the mkrlconf.sh script that comes with rEFInd. Thereafter, you should be able to boot with rEFInd without entering the boot options. This method bypasses GRUB, so you can optionally remove it.
• Re-install Linux, being sure to install it in EFI mode rather than in BIOS/legacy mode. Mint's installer image file doesn't boot properly in EFI mode from a USB flash drive, but I've heard that UNetbootin can create an EFI-bootable USB flash drive, so you could try using it, or you could use an optical disc instead.

I solved this by creating a bootable USB flash drive with UNetbootin and installing Linux Mint in EFI mode. After disabling secure boot in my BIOS settings the GRUB EFI was loading successfully. I use rEFInd as a boot manager; it is simple to install and works without a hitch.