This may be impossible. I shot some footage of shorebirds at a low angle, and, too late, noticed a dark blurry shadow passing back and forth over the scene. It was an out-of-focus blade of grass waving near the camera. Can this moving, dark, blurry but transparent shadow be removed. It certainly could be in Photoshop, but that's frame by frame.
yep- post a frame or the footage lo rez and we may be able to give more advice. Depending on how big the shadow is, how fast it moves and the complexity of the background there may be several things you can do.