One leg swings up while the stays in the neutral position when swinging the legs.
The leg that was in the up position then goes down to the neutral position and the other leg starts swinging back to create momentum before it swings up.
The switch happens when the legs are both in the same position.
The first leg that went up then pulls backwards and the other starts going up.
This reference really helped with the animation for the last scene and is also good research to widen my knowledge as to how the legs would move when its swinging from an overall static body position.