Aren't a lot of her comand moves called like swallow drop or swallow tail, wings, rising swallow, etc.
Plus her theme in 02UM mentions a swallow with a dragon and tiger. So I'm assuming she's the swallow and Ryo and Robert are the dragon and tiger.
But I think her DM is called flying phoenix kick or something like that. So she could be a Phoenix.
If I had to make up a title for her it'd be Heavenly Phoenix or Graceful Swallow.
Phoenix to put her on the same level as Ryo and Robert since dragons and tigers are supposed to be hecka big pwnz3rs in Asia. I don't really know asian mythology that well, but I can't recall hearing anything about swallows...
And everyone in KoF XIII calls Mr.Karate the Legendary Karate-ka. So I'm going to assume that's his title. But then again, he refers to himself as a demon, so it could be something around that. Like Unstoppable Demon or Raging Demon. =p