Leopard Fist is a style you cannot learn in vanilla Jade Empire, but you certainly see lots of it. This is the "brawler" style that sailors and pirates use against you all the time. It's supposedly simple, unsophisticated and unworthy of a Martial Arts Master such as yourself.
It's also exceptionally dangerous. Not so much when used by those simpletons, but expertly used, it is at least as good as the standard styles. I find it particularly useful for sidestepping and interrupting weapon attacks. But that's just me.
Martial Style This style can complete a Harmonic Combo. Leopard Fist is similiar to White Demon in many ways. Both styles are rather slow, but have a long range and do huge amounts of damage. Why White Demon is taught at the most prestigious schools of the Jade Empire, while Leopard Fist is more likely to be seen in a teahouse brawl, is unknown. Some of the White Demon grandmasters claim however, that their chosen style can only be truly mastered, if it is combined with the mastery of Leopard Fist.
I've heard people say, that Martial Arts aren't all that useful anymore in the later chapters of the game and that it's better to switch to weapons instead. I beg to differ:
Beating up the Ravager with Leopard Fist
A word of caution, though: This may be slightly more difficult than it looks.