The reverse somersault for The Last Ninja was at some point documented on Kai’s website, The Last Ninja Archives.
Having not seen the reverse somersault myself, I was looking for a trail leading to it within the animation sequences. There is something at frames 28/29:
Frame 29 is different from the one used for a common somersault, 26, in which Armakuni is higher up as indicated by the distance between his body and its shadow:
I haven’t done specific research in this sense within the code, but if you’ve ever made a reverse somersault, please feel free to leave a comment!