13'' MacBook Pro 2010 stuck at blank gray screen, no boot option working
Since you are talking data recovery now, until you get all your data back DO NOT WRITE TO THE DRIVE YOU ARE RECOVERING UNDER ANY CIRCUMSTANCES, EVER, OR YOU WILL LOSE ANY AND ALL DATA ON THE DRIVE WITH ABSOLUTELY ZERO CHANCE OF RECOVERY!!!

If you really want to play it safe you should send your drive to a data recovery service. Those are expensive but you have a better chance at getting your data back. A good data recovery service can not only get data out of a drive with messed up metadata, but also a drive suffered from mild to medium damage.

The best bet without contacting a data recovery service is to boot from another device and image your drive off to another storage media. Then you can try to mount the disk image and fish your data out of it. Some Linux-based tools can be very useful.

I would suggest against using that drive ever even after you have recovered all your data. That puppy have suffered from some damage and will have a shortened lifespan. For laptops since physical movement is a daily occurrence I suggest you get an SSD for it. Not only will your laptop load faster the SSD is virtually immune to most physical trauma that can damage a hard drive so it will survive longer. By the way you can force TRIM under El Capitan so there will be no long-term speed and lifespan penalty.