With hardware data loss (physical damage on the disk), the more you fiddle. the more you lose. Unplug it and send it off to the experts with a clean room. They disassemble the drive, clean the platters, mount them in another drive and then read off all the data, sector by sector, with multiple passes and retries on the damaged area until they cannot get any more back.
Now a few years ago, but full recovery and a $3K bill for a Seagate HDD. Boss said the data was mission critical, and was happy to write the check.
For a software data loss, I have also used Recuva with good results. As long as you do it fast, before the data has been overwritten. In that case, all is lost unless you have a backup, a backup that you can restore - something that a lot of people do not test until it is too late.
Vatican bank IT department motto: Jesus saves, so should you.