As a master of both the sword and magical arts, Karin is well-used to fighting all sorts of bizzare creatures. A phoenix, while interesting, is not such a big deal compared to all the creatures she's had to face in the past. Karin's speediness will be helpful here, keeping the battle going at her own pace. Her sword strikes will make quite a dent in Peter's HP, and his own attacks, while strong, are somewhat offset by her own natural regen. This should be enough to outlast the bird's own meagre defenses. A few hits here, a few hits there, and Karin should have no trouble in taking care of business and scoring a victory over her worthy, if significantly weaker, opponent.
