If the hydraulics were strong enough to twist it back, that would mean the metal and/or joints are so fatigued it will no longer support the rated capacity and needs a lot more work to be ready to use...
Seeing where something needs corrected is really only necessary if you can't see how it was damaged. Considering it took a hit to the bucket, perhaps chaining the bucket to an immovable object in the area of the impact and reversing the tractor to get a pull opposite of what the hit caused could pull it back out. If you can see how it was damaged, many times trying to "reverse" the damage is easier than "repairing". I would consider the bucket to be scrap. Drilling or welding on it to put an anchor to pull from the main point of impact shouldn't be an issue.
If it does come down to IDing the bends for repair work, you may be able to inspect the paint/powder coat all over the unit for any signs of cracking. That will be the area that bent. Being black, you could even rub it down with some old Turtle Wax paste to help locating any hairline cracks. Cracks in the finish may not appear immediately.