Unfortunately a lot of the time, a child who's victimising another child will be projecting emotions that they're feeling, due to abuse / difficulties they're experiencing themselves.
To think that the problem can be hugged out is crazy - it's not going to happen.
I think the first most useful thing to do is to teach the child to fight back. Often a change of attitude - being able to have the confidence to say 'no' and to stand up against adversity, is enough to change the tack the abuser's behaviour. Violence isn't necessary - and I don't think it should ever be encouraged .. but taking a stand is an entirely valid response.
But secondly the root causes of the abuser's behaviour do need to be looked at - and a simple response isn't going to solve these problems. It would be nice if the simple idea of 'punishment' could resolve the behaviour - because it would require minimal effort - but realistically it wont.
Reforming bad behaviour involves understanding what the person involved needs - sometimes that will be love and understanding. All children have complex emotional and psychological needs; if these needs are neglected, something has to give .. and usually does.