Chiu Mun wasn't exactly someone you could call an elite fighter from HEAVEN SWORD & DRAGON SABRE. That being said, she seemed surprisingly good for someone of her young age, limited experience, and unorthodox training. Several times during HSDS, she performed surprisingly well against much more powerful enemies. For example, using the Heaven Sword, she was able to give Granny Golden Flower a decent fight. Although Chiu Mun obviously had a superior weapon, Granny Golden Flower's martial arts were more than superior enough to make up for the difference. Nevertheless, Chiu Mun put up a good fight (although she would ultimately lose if Granny Golden Flower were to press the fight further). Later, when Chiu Mun helped Cheung Mo Gei fight off the three Persian Ming Cult elders, she proved surprisingly helpful. She was by far the weakest fighter in that battle, but she held her own and was able to help (she wasn't completely irrelevant out there).
As a member of the Mongol nobility, Chiu Mun had access to all kinds of martial arts teachers. Certainly, there were the Yeun Ming Elders, the Diamond Men, and maybe even Sing Kwun to train her. By having so many martial arts available to her, however, she might have run into the same kinds of problems that the young Gwok Jing did when he was trying to learn the diverse martial arts of the Gong Nam 7 Freaks, or that young Yeung Gor did when he was learning all kinds of disparate skills during his youth. Like the early martial arts of those two heroes, Chiu Mun's martial arts training must have been broad, but not particularly deep.
One final observation: Chiu Mun seemed to have photographic reflexes. She was able to imitate Kunlun Sect Leader Ho Tai Chung's sword technique after observing him exhibit it once. Unlike Cheung Mo Gei, Chiu Mun did not have a special skill such as Keen Kwun Dai Loi Yee to instantly replicate an opponent's martial arts technique. She seemed to be able to do it on instinct and reflex. This is quite a talent.
Did Chiu Mun have it in her to develop into an elite martial artist (given the proper training)?