First seen in a 1991 issue of Electronic Gaming Monthly, actual footage of the unused sphinx mid-boss from Mega Man 4 has been discovered! You can see it rises to the surface at the 4:13 mark in the above video.
Bits and pieces of the sphinx's remains have been found in the retail version of Mega Man 4, but this is our first time seeing the thing in action. It's never been specified why it was cut from the game, though seeing it now I wonder if it was too difficult to beat. Presumably, players were to jump on top of the boulder to shoot the snake on the sphinx's head. However, Mega Man himself has very little room to maneuver. Unused sprite data provides credence to the theory as the boulder was decreased in size later in development. Ultimately the entire boss was cut.
This footage comes to us from Robert Hoskin, who filmed it in May '91 with EGM staffers Ken Williams and Edward Semrad. I suggest you keep watching after the sphinx's appearance; there's lots of other Mega Man 4 beta elements to see!
Thanks to NintenCade360 for the tip!