I am writing for my school newspaper and I would like to know if it is right to bully a bully?
Two wrongs don’t make a right.
You never put things like that in a school newspaper.
Is your newspaper a newspaper or a gossip column? Don't you have a faculty ad user. Ask them this question. People have gone to jail for defamation and internet harassment when someone commits suicide because of internet harassment. Your school could be legally liable.
In both high school and college, The NUMBER ONE reason students have trouble writing ANYTHING is because they try to write off the top of their heads -- without first LEARNING anything about the topic. Good journalists do research. Find 3-5 academically-acceptable resources (the librarian is your friend), and do AT LEAST 2-3 hours of study, taking notes as you go. Then, try again.
Sure, we do exactly that over here
If bullying is wrong - then it is always wrong. To bully a bully is a form of revenge and revenge is also a hateful concept that never results in anything worth while.