It's possible, but you would need about 16 gigs of ram, a killer video card, and your Host OS would need to be X64 Windows, e.g. Windows 7 X64 or Windows 8 X64. And you would want something like Windows XP for the Virtual Machine (before driver signing).

Get Virtual Box, Install it.

Create a Virtual Machine, Install Windows XP to it. Enable direct 3d in virtual box.

Install FFXIV on the Virtual Machine.

Copy the virtual machine's VDI/VHD image, use

vboxmanage internalcommands sethduuid "imagename.ext"

Create a new virtual machine using the copied image.

Run Both VM's at the same time, put one on each monitor, run FFXIV * 2.