What is the ruling on remaining with female teachers who are immodestly dressed and exhibit inappropriate behavior, given the urgent academic need for them?

It is not permissible to take tutoring lessons from female teachers. Rather, what is obligatory is to abandon that and seek safety for one's religion and honor. One can search for qualified male teachers, for Allah Almighty says: "And whoever fears Allah - He will make for him a way out And will provide for him from where he does not expect."