Okay, I’m in a certain AP class that’s really good. I am having no trouble with the material, but I hate the teacher. (S)he is pretty mean and treats me like crap and gives out nothing but busy work. What I plan on doing is stick it out this semester and then drop the class next semester (maybe to a different AP, maybe to Intro to Engineering side note: is that a college credit class?) and self study for the AP exam and take it. Does that look bad for colleges?
Colleges don’t look as favoritly on self studying as actually taking the class. From what I heard, they really don’t care all that much. So that would make it about the same as taking any class and dropping it because it is too hard.
If you take the AP exam AND replace the dropped class with another one (Intro to Engineering is fine, for instance. And don’t forget to take an art course, especially if you hope to attend a college in CA where it’s a requirement.)
However, what is this class? For AP Stats, your plan shouldn’t be a problem. For AP Euro, however,it’s likely to really be a timesuck for you.
The class is AP Physics C. First semester is Mechanics (which I can pass by in a breeze) and second is Electricity and Magnetism. I plan on just taking the Mechanics test as E&M would be too expensive for me. And I keep hearing how the teacher gets really mean during E&M.
Oh and thanks, @Madeline25. I’m taking that into account.
You’re lucky - just take the Mechanics test indeed. 
I would instead suggest you have a honest discussion with your teacher about this, let her know what you are feeling and thinking about, and ask her if she thinks it is in your best interests.
Chances are that her respect level for you will increase dramatically. And your self-confidence will improve a LOT by proving to yourself you can act like an adult.
You might also consider talking to your guidance counselor for advice here - someone more familiar with who this teacher is.
And for the record, lots of kids across the country find this AP course to be heavily loaded with busy work.
I totally understand you. Last year, I was in a class and my AP Spanish teacher was so horrible. She did everything she could to ruin my grade.