When bad sectors appear on a disk all of a sudden, that means its hardware failed. The best thing to do is to go to a data recovery professional with proper equipment and expertise. Do-it-yourself data recovery rarely yields something meaningful in such cases. For your case, for example, data recovery professionals have special hardware disk imagers that can, through some certain tricks, read even bad sectors. Yes, that costs, but there's a good rule of thumb: if the problem is easy, you'll wont pay much, if it's hard, you won't be able to solve it yourself.
Still, you're right using R-Studio for data recovery. You need to open the image you created using R-Drive Image. See on-line help for assistance: Images
then you need to scan the image: Disk Scan
, then recover files Data Recovery Using R-Studio
/ Your case is Case 2. Recovery of files that have resided on a data disk with a damaged file system, or on a previously deleted or re-formatted partition.
Frankly, I doubt that will bring some success. Still, that's worth trying.