Did you capture a screen shot of the HDsentinal screen ? If you did then could you post it so we can check some things. I want to see if the weak sectors/bad sectors are just a few or 1000's. If it is in the 1000's you need special software and hardware to work with the drive as BC_Programmer said you will need a specialist data recovery company.
HD sentinel is a hard drive diagnostic/information tool, it doesn't do drive copying.
For windows drive copying, making an exact copy to a file or larger Hard drive which you can then recover from. one option is
https://hddguru.com/software/HDD-Raw-Copy-Tool/Windows is very hard on drives when copying bad sectors trying 100's of times to read a bad sector. Specialist tools and Linux can ignore bad sectors, copy the good sectors quickly and then go back and attempt to recover as much information as possible from the bad sectors focusing only on the sectors with data. The software can then report on the success and what files may need reloading.
The first thing though with any hard drive fault is to diagnose what is wrong and know what steps to take to get the desired result.
I'm sharing this as it only applies to mechanical drives.
SSD's require a different method, if users monitored either with the tools supplied by the SSD manufacture or programs like HDsentinel then Data recovery would not be necessary.