I'm not an *experienced" instructor, but hopefully an experienced pilot who does some instructing.
Firstly, asking what the hard bit is suggests there's an easy bit - well if there is, I've still not found it.
But doing odds and ends of specialist instructing - conversions, currency and the like, I find the most intellectually tough bit determining the actual training needs of any particular student.
Close behind that is trying to make safe, private pilots who have been taught badly then re-inforced those bad habits through a few years of solo flight.
G