have you ever installed Linux Mint before? I just dual-booted Mint 14 with Win8 UEFI last night, and the only thing different was at the end, my Asus would only boot straight into Windows, as if I never had installed Mint. But I ended up fixing that with the Boot Repair program that comes with Ubuntu 12.10 Secure Remix, which is made to be able to deal with dual-booting on UEFI.
It is a bit much to write out here, so it might be good to find a basic installation guide here, and then the last part is hopefully a pretty easy fix. well, it was easy once I found out to use Boot Repair in Ubuntu 12.10 Secure Remix
also it looks like other secure boot/UEFI solutions are popping up in the forums, etc.