Arya Stark encounters the waif in the dark while she has the needle in her hands. She becomes successful in making her feel that she is weak and wounded, however before it she was trained well, being a blind and then blocking the lethal attacks of waif.
She took the advantage of dark and slayed the waif. Later Jaqen H'ghar terms Arya as no one, but she knows her real purpose. She tells him that a girl is Arya Stark from Winterfell.
Though what we did in video was to amuse viewers more rather than help them reach the reality because the reality is clear, How Arya killed the waif?