Since you didn't tell which backup program created that file, it's impossible to tell which program could posaibly repair it.
But the prospect is bad. My guess is that it is some custom format, and that only the maker of the program can offer support. And I'm afraid it won't be free, but that depends on their support policy. It's up to you then to decide if the value of the "very valuable" data is higher than their quote. If, for example, the value of that data is $1000 and you have to pay them $2000, it obviously doesn't make much sense to have it recovered.
This, by the way, is exactly the reason that we advise to stay away from backup programs that use their own proprietary format for the backup file. Just making a copy that you can read in Windows Explorer or Linux without using special software is the way we recommend.
Finally, let me remark that a backup only is useful if it can be read. So it's bad practice to delete the original without being sure it can be restored from the backup. The risk of losing it is just too big.
Recently I faced a system crash down. All my data including the main backup file has damaged. I had the same backup copy in my external hard drive. So I formatted my system and tried to restore my data from the backup present in external hard drive. But I couldn't do so as it was not opening. This error stops me "the backup file contains unrecognized data and cannot be used". Is there any method or an application which can repair this backup file? I can't afford such data loss. My data saved inside the backup file is really very valuable for me. Please help.