There may be multiple variations of this (along with all other Dailies) Quest.
Mine in particular states i needed to kill 100 via Basic Attacks, but i did not start accumulating quest progress on this Daily until i started killing them with Special Attacks instead.
EDIT: I did some more testing while i had the Daily Quest still active, and it's not broadly just "special skills" -it has to specifically be Soul Force skills.
In otherwords, any skill that uses the Soul Force (SF) resource- i tried using the "Cooldown special skills" and those did not work.

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While your version you ran into pushrbx very well may have needed different requirements, but as you mentioned- stated otherwise in the quest description.





