Firstly, I would have had my kid involved in extracurricular activities, had them assisting in chores and other things, and developed in them a sense of self-reliance and independence.
I did plenty of chores and sport and it never solved any bullying problems for me.
Such self-reliance would include self-defense classes; No girl should fear that a boy will assault her.
Given opponents of equal fighting skill the larger will tend to win. Not always but it's the way to bet. Being trained to fight to a higher level than your potential opponents is a good way for an individual to overcome bullying but on a larger scale won't solve bullying but can change who the bullies are. There is also a lot of bullying that isn't physical. How do you use self defense classes to combat embarrassing pictures on facebook?
Secondly, I'd track down the parents of the child bullying and explain the situation to them verbally and in person. If the parents didn't step up to the plate, I would explain to them in a non-verbal way my disappointment in their lack of parenting.
If I'm angry enough to fight someone, they're going to be facing me and they're going to be armed. And then they're going to lose.
So you'll talk to the parents and if they don't respond to your satisfaction you'll fight them to the death? Unless I've misunderstood, I think you need to revise this plan. If you win, it ends with you in prison and bullies doing whatever they like to your child while you are occupied with much tougher bullies.