(Some of the meaning might have changed, I tried to guess the intention in a few places and I've broken it down line by line. Let me know if you wanted to say something different!)

I will mock her stupidity.

I will be successful and show them how stupid they are.

(The first two parts are fine, these are just my own word choices)

In recent years I have learned how to handle the unexpected, that I am able to solve problems, and that I am strong.

(I'm not sure if this is what you mean. I can try again. You could also say, "handle unexpected emergencies." I also chose "strong" instead of "hard")

If they want to pick on me, I will make them regret it.

(Or, "They want to pick on me. I will make them regret it." This sounds even more serious to me if that is what you want. The second part could also be "I will deliberately make them regret it," but I think making someone regret it is already understood to be deliberate!)

If she wants to beat me, she will need to put in 10 times the effort as me. Don't be a lazy and stupid person anymore.

("wants to be a winner" is fine, but I think you are talking about a direct competition between the two of you. Also, you generally "put in" effort.)

I know it's impossible for her, so I will be the winner and mock her failure.

(Looks good!)