The most efficient way is to find a Live Windows image and boot from it.
You will be able to flash BIOS from it.
But beware that in some cases it is not a good idea to flash a new BIOS. About a week ago I flashed a new BIOS to an Asus laptop using a BIOS utility (built in into BIOS called EasyFlash).
After that I lost touchpad in Ubuntu and had other problems. I couldn't downgrade BIOS using the same utility because it didn't allow to flash older BIOS.
So I had to use a Live Windows image where I successfuly downgraded BIOS using
So if you don't have a very strong reason, and everything works fine, don't upgrade BIOS. Ubuntu will take care of CPU microcode.