I would argue that it is Arrow's relationship with the cellist, a man she has never met but has been ordered to protect, that develops her character. As our story starts, Arrow is a young independent sniper who is posing a significant threat to the men who are hellbent on destroying her city. It is a role that she had taken on reluctantly after her talents had been noticed while she had been a member of the university sharp shooting club.
Arrow is assigned the task of protecting the cellist, who is attempting to bring some beauty to the war-torn city by means of his music. She finds the music hauntingly beautiful, and even after an attempt is made on her own life, she is not deterred from her mission of protecting him. Even when she locates the assassin, and feels a moment of kinship with him when she realizes that he, despite his assignation to kill the cellist, is spellbound by the music.
Arrow and the mystery assassin share a moment, during which they are united by the music and neither wants to take the other's life. However, Arrow's loyalty to the cellist comes first, as it her relationship from a distance with him that has changed her perception of the war. She therefore takes her shot with the precision for which she is renowned.