Running Time Mechine Backup from Recovery HD
The Recovery HD doesn't have the ability to make a backup other than using Disk Utility or the terminal app to copy files.

If you have a spare HD available or don't want to risk reinstalling the OS (which isn't designed to delete any user files - but could if there is directory damage) I would say go buy a USB external drive and reformat it as GUID/Mac and use Disk Utility to "restore" the boot drive to the external drive. Then you can run the OS installer from Recovery or erase and install.


Reinstall Mac OS X Mountain Lion before selling a Mac
https://support.apple.com/en-us/HT204904