If someone has wronged you terribly, and has not asked you mechila because she believes she has not done, and does not do anything wrong, am I required to forgive her (it is very difficult, as these things she has done have been very severe, such as slandering, false accusations, holding back from giving promised money etc…) This woman has been brought to countless rabanim, yet still she believes she has done nothing wrong. What is required of me?
The moral requirement to forgive somebody only applies when he/she asks for forgiveness. There is no obligation to forgive when the offending person is unrepentant.
Sources: See Rema 606:1; see also Gilyonei Ha-Shas, Yoma 87a, who discusses whether or not there is an actual obligation to forgive one who asks for forgiveness, or whether this is only worthy conduct. See also Sefer Hateshuvah 2:10 who derives from Rambam that the obligation to forgive only applies after somebody requests forgiveness three times. See also Shulchan Aruch Harav, 606:4.