I know this is just a cartoon from a Hey Arnold episode but this must be a dumb reason to beat up someone. They are always going to be people that simply don't like you.
Besides why would anyone want a reputation of beating up others?
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They're in the same grade she's 14 and Helga's 11 she's not that much older and it's because she failed a grade. Helga shouldn't have talked about her in the first place she deserved what she had coming to her and she still didn't bet Helga up.
Patty is actually pretty nice besides letting Helga go and giving Arnold the last pudding there was another episode when her and Ronda began attending a public school and Ronda was mean to her but she agrees to tutor her so she could be friends with her.
Patty may seem like a bully but she isn't and the only person that new that from the beginning was Arnold. The lesson of story is to not judge a book by it's cover.1