In about the first five levels, it is easy to get the other three special move achievements. However, even though the Nightwatcher is Raph's alter ego, the game recognizes them as two totally different characters. If you used his Power Climb while playing as the Nightwatcher and wondered why you did not get the achievement, it is simply because you were not playing as Raph (even though, technically you were) and the game saw you as the Nightwatcher.