"My bad" is slang for "my mistake".
Key word: slang
So... is slang = bad English?
Personally, I feel you can't keep slang (and other similar 'mangling' (for want of a better word) like Singlish, SMS Lingo, etc) out of language. What is important is to recognise what is slang, etc and to NOT use it in formal communication or in situations where readability by users with different English language skills is important. And it is important that we teach our children that too.
Anyway, you were reading fiction base on a popular cartoon. I would assume it had little or no emphasis on English language education, and I would not expect the language used in it to be formal or educational.
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