If you were to attempt it, you would need a stud gun. Hammer and dolly would be secondary and access is limited in many places. In addition to pulling up lows you would actually use the stud gun as a dolly, holding tension on it in a low and hammering the highs around the low.
If you have little to no experience though, it would be better to replace the bedside. It's more straightforward. But if you want to learn then try repairing it. Go slow, don't start slugging it out from the backside and make a bigger mess. Work out gently what you can from the backside. Then using the stud gun. start with the lowest areas, gradually working them up with the stud gun. Use the weld studs for leverage to work down the high spots. Go easy, work slow, gradually pull the lows up. Use your hand to feel the lows and highs.