Execute the following (replacing __PCI__ with your cards PCI, for example, 0000:02:00.0):
The VGABIOS will then be in your home folder.
echo "1" > /sys/class/drm/card0/device/driver/__PCI__/rom
cat /sys/class/drm/card0/device/driver/__PCI__/rom > ~/vgabios.bin
echo "0" > /sys/class/drm/card0/device/driver/__PCI__/rom
(You should however check the vgabios with your favorite hex editor to make sure it's the vgabios in there, and not an error message, for example. Or "cat ~/vgabios.bin", you'll notice if it's the vgabios or not)
However, there are also other methods, for instance ATITool (Win64/Win32/Dos) etc..