A bad grade can seriously damage your college application. Sometimes bad grades come without a particularly useful explanation; they are simply the result of a failure to work at the appropriate level for the course you’re taking. But some bad grades are the result of situations beyond your control. In those instances, it’s worth taking the time to provide the admissions committee with the context to understand those bad grades.
Malady or Other Ailments
In the case of illness or surgery, you should address this situation and not allow your application to suffer without giving the appropriate context. For example, illnesses such a mononucleosis can make it difficult for even the most diligent students to keep their grades at their normal level, as can surgery for significant injuries or illnesses. If you have poor grades one semester as a result of an illness, let the admissions committee know.
An extreme change in your living situation that has made it difficult for you to perform in school is also a reasonable explanation for poor grades. For example, an serious illness or death in your family might lead to increased responsibilities at home and substantial emotional turmoil, the combination of which will almost certainly impact your academics. Similarly, sudden financial changes in your family might require that you work after school (or increase your work hours if you already have a job) which could also impact your grades.
How to Approach the Admissions Council
How do you communicate this context to the admissions committee? You write what is called an addendum to your application. Do not use the main college essay to address this issue. There is a portion of the Common Application where you can inform colleges of "Anything else you want us to know" which is where you can provide any necessary context for poor grades..
Please be aware this is not an opportunity to make something up to explain away a bad grade that is simply the result of your not doing your best. College Admissions officers can tell if you’re making things up from a mile away. This is not the time to play games and put your college acceptance in jeopardy.
In conclusion, if you wind up in the dreaded situation of a personality conflict with a teacher and that conflict leads to a poor grade despite your best efforts, there isn't much that can be done. If this teacher’s reputation is known to your college counselor, you may want to bring it up with your counselor and see if there's any way it can be addressed in the counselor’s write up that is part of your application. But you will probably just have to grin and bear it.