I don't know what's going on but dailiy HC and weekly LFR are not counting towards the quest. Of course I did them AFTER I acquired the said quest. I don't know is it designed like that but if it is that means you will have to do 120 dailies a week + all of the 16 bosses on normal to reach that cap.
I really, really hope that's a bug with HC and LFR not counting.