Much too much telling, and no nearly enough showing.
Split this "one" chapter into three or five chapters, and expand them,
so that little or nothing is *told*, and most or all of the events are
*shown*.
Ranma 1/2 is a comedy-romance, and your story is not. Where are the
fiances fighting over Ranma? At the very least, they would all want to
nurse him back to health after he was left for dead. Ranma's not yet a
high school graduate... Hinako and Kuno would be after him, too.
You've got no character development, you do relatively little to show
the hard work and effort that Ranma puts into learning this new art.
Why would Cologne tell Ranma of the existance of a style which could
counter the Southern Cross style of Shin? After all, she does want him
to marry Shampoo and father some great-great-great-granddaughters for
her to train, and if he goes out and does this, he could end up dead.
Why does Ranma immediately go after the North Star Successor, rather
than trying to improve in ways that don't require so much travelling?
Just because Cologne *says* that's the only way to defeat Shin, doesn't
mean that it *is*.
I don't know the Fist of the North Start storyline too well... what
kinds of ranged attacks does Shin have, that he might use to counter
Ranma using Moko Takabisha or Kijin Raishu Dan from a distance?
Where's Ryoga in this story? Has he fallen off of the face of the
earth?
Giving Ranma the ability to kill and heal with ease makes him rather
overpowered -- before, his ego was merely big, now it should be through
the roof. Not to mention, if he's too strong, any physical conflicts
will be rather one-sided, and conflict is the heart of any good story.
What you've got isn't really a story, it's an idea with a few scenes
written out.