Repair or reinstall Mac partition
It all depends on what is going on with the drive and unfortunately there is really no good way to tell.

I have been using Diskwarrior for YEARS and it is still my go-to disk repair tool. Drive Genius is pretty good too. I have both but always start with Diskwarrior.

These tools MIGHT be able to repair the volume issues, but it might be quicker, easier and cheaper (?) to just bite the bullet and do what the disk utility says: reformat and reinstall.