If I were you I would be very careful. If you really want to retrieve the data you shouldn’t do anything with the disk, especially no write operations. You should take a look at testdisk and photorec. These are the best programs for recovering data. testdisk is for recovering system partitions etc. whereas photorec is for recovering documents, photos, videos, etc.
If I had your HDD it would be probably easy for me to recover the data, but on the other hand it is hard to explain to you how exactly to do it in your specific case. Well, if the data is like super mega important to you, then you should really sit down and read the documentation and tutorials for these tools for a couple of hours and then you will be able to recover the data yourself, I am sure. If you will take this path, here are some more helpful tools:
I use these and a couple of lesser tools for when I recover data from HDDs. It’s not easy to get into it, but if you really really need the files and don’t want to pay thousands of $$$ for some foreigners to do that job, you should do it.