Boot up with a live cd, or ubuntu CD from a different partition.
Mount your feisty drive somewhere in this example i am mounting on /media/feisty
Create a directiory when do you want to mount
sudo mkdir /media/feisty
Mount your drive using the following command
sudo mount /dev/sda2 /media/feisty
(replace /dev/sda2 with name of drive, e.g. hda1 etc.)
chroot into your feisty drive.
sudo chroot /media/feisty su
Update your system via apt as normal. (sudo is not required)
ctrl+d or type "exit" to exit the chroot, then reboot the computer and you should be able to get back into feisty.
Sometimes there will be no Internet connection in the chroot environment.
To correct this, we have to enter
sudo cp /etc/resolv.conf /media/feisty/etc/resolv.conf