A good program for recovering data and partition table(s). Install from package management or command line, like
sudo apt install testdisk

Usually used via liveDVD or USB or hard drive bay (like in this example). If using via liveDVD, mount external hard drive using sympolic link to your $HOME directory. An example live mint

ln -s /media/mint/"external media name here" /home/mint

When finding corrupted damaged partition, press q and select next partition, and so on. If wanting to copy files, the path fo files is /home/mint/"external media name here", as the symbolic link for the external hard drive leads.

Basic commands
p = list files (print)
q = return back (quit)
c = copy
a = all
C = copy all selected

Arrows left and right are giving options for partition table, which is allowed to write when selected partitions are green.