Walk to the right until you reach the door. Enter it. Don't try to walk farther to the right, because the platform will disappear and you'll fall down. When you reappear, walk to the left, avoid the ball, and head onto the elevator to get taken to the door. After that, go up the two elevators, destroy the two flashing blocks, and then ball that will likely be coming at you. Once it's gone, continue to the left, up the ascending platforms to the door at the top. On the other side, there will be a ball waiting. Destroy it and head up the elevator. When you're at the top, carefully wall to the lower platform and destroy the ball.
It's better to get rid of it when it's coming toward you rather than it going away since it will likely reverse direction once you fall toward it. After it's gone, head to the left, and up the elevator at the other end. Take the elevator all the way to the top and then jump to the right. If you don't the platform will disappear and you'll have to start over. Once you're on the other side, quickly walk into the door and then to the left through the other door. Wait for the eye to float back to the right before you head onto the elevator or you'll get knocked off. When you reappear, head through the door to the right to finish the stage.