Towazugatari ~Shoujo Ryoujoku Hishou~

Kirino Ryouko had her father, mother and beloved brother murdered by monsters in the past. She hates demons more than anyone and that's why receives exorcist training to fight them.
One day she is dispatched as a teacher to a high school where beast is noticed disguised as one of the students.
At school the most beautiful girl gets targeted and then violated by a group of hooligans possessed by spirits. Taken photos are used to blackmail her and repeat this hell on daily basis.
Eventually teacher and student meet and prepare bloody revenge.

[From vndbreview]