Ни в каком режиме не засчитывается выполнение задания, хотя пропуск куплен и уже напрямую прохожу битву, которое предлагает задание
Ideas
You need to complete Galactic Challenge feats. The current one is in the Events. It's Inquisitors Vs Galactic Republic. Just completing the fifth tier will earn you the Episode Quest.
Edit: if you've already completed that, you'll have to wait until the next Galactic Challenge.