One thing you need to remember about this sort of motion is that you should never really be thinking in straight lines. If you observe the way the legs move, they don't scissor back and forth on vertical paths of motion; they rotate at the joints. Almost all motion of a bipedal figure, even if it looks vertical, is actually taking place on an arc. Watch as the back leg lifts between frames two and three; it doesn't glide through the air diagonally in a straight line. Instead it pivots from the hip, while the knee traces an invisible arc of motion on the air. Try bending your leg at the knee and then lifting it up from the hip, and trace the path of motion of your knee with your eye; it will form a curve, rather than a straight line.
You can see it more clearly if you raise your forearm straight before your face, with your hand palm inwards and flat; "chop" your hand to the side without twisting it, moving your forearm at the elbow, and the arc of motion that your fingertips trace will be easy to follow.