HDD disk utility first aid failed

It sounds like you’re disk has got physical surface defects. File system repair utilities are of limited use in such cases. Take a look at Advanced Hard Disk Tools in the Restarters Wiki.

Unless you can boot your iMac into Linux and DOS utilities (I don’t know whether that’s possible) you’ll need to take out the hard disk and temporarily attach it to a PC. There are 2 possibilities:

Spinrite can often recover unreadable sectors by doing its own error correction on the aggregate data accumulated from many reads. It’s far more persistent than any OS or the drive’s internal error recovery logic. If it succeeds it’ll remap the sector. If it was a transient error from a physical jolt or a voltage spike during a write and the disk is otherwise in good health, you can continue using it. However, Spinrite costs $89, but you get a lifetime personal licence and a money back guarantee if it disappoints.

If you can boot into Linux of any flavour then ddrescue will clone your hard disc to another. In a first pass it’ll read everything it can and keep a log of any sectors it couldn’t. You can then rerun it as many times as you like and it’ll just retry the sectors it has so far failed to read. This is a good option if you fear your disk is could die completely at any moment, allowing you to recover as much data as possible while you can. After the first run, running Spinrite might well enable it to succeed completely on a second pass.

Or, you could just find a professional data recovery firm. For a 3-figure sum they should be able to get your data back if it’s humanly possible, and should only charge if they succeed.