What's he mean by "hurt in the right way?"

Native speaker’s answer
Rebecca
This is a bit of a joke. Dr. Doof here is implying that there is a "right" way to emotionally hurt someone, which he describes immediately after. You can understand it as the typically, preferred, or expected way to hurt someone. This is not an expression that is used, it's just a bit of humor added to the show. Indeed, any method used to hurt someone is wrong and cannot really be described as "right."