The problem? Recovery mode defaults to a read-only filesystem. Video driver installation requires creating temporary files, but temporary files require a writeable filesystem. The result is that the video drivers refuse to install.
Here is how to change the recovery mode filesystem to read-write at the root prompt.
1) First, open the GRUB boot menu by holding or tapping the right shift key on the keyboard when the system boots. It might take a few tries since it sometimes seems to skip the right shift key if it is not pressed at the correct moment.
2) In the GRUB boot menu, choose the Recovery Mode line of the kernel you wish to boot and press the Enter key on the keyboard.
3) Linux Mint will boot to a text menu. Choose “root” (Drop to root shell prompt).
4) At the password prompt, enter the system’s root password to log in, and the root prompt (#) will appear.
5) Enter the following command:
mount -o remount,rw /
Press Enter, and that’s it. The filesystem is now read and write. Be careful of what you do at this point because you can damage your Linux system. When at the root prompt, you are doing everything as the root user with full privileges, so there is no need to enter sudo.
Make sure the video drivers are already in the root directory so you can install them without having to navigate to a user’s directory to find them. This saves time.
When finished, press CTRL+D to return to the text menu for a normal boot, or enter the command reboot to reboot the system.