You haggle over something when you're negotiating something, like a price or terms of a deal.
I haggled with the butcher over the price of the lamb chops.
You can complain or whine to your friend about your grades.
You can haggle over a grade with your instructor if you try to promise to do extra work for a higher grade or anything that involves negotiating a higher grade.
This word has negative connotations. If you're haggling here (in my part of the world), you're being petty and annoying.