[X] Yato's Plan: Essentially? Just chase the Bakeneko down. Yes, Hiroko said not to do that, but Yato is confident in your abilities to resist illusions. You've trained all this time to accomplish that feat. Now it's time to put it to the test.
[X] Hiroko's First Plan: The Bakeneko can use illusions. So can Hiroko. Thus, she'll match her power against the cat's. If she can manage to overpower the Bakeneko's own abilities, she could trap the cat in an illusion of her own making. This would make it much easier to catch her.
[x] Hiroko's Second Plan: Hiroko's a fox. While not as good as a full dog's sense of smell, she can use it to track down other animals. This includes cats. If she can get the scent of the Bakeneko, she can lead you both to her location. Though...she did say she hadn't eaten recently. And you're not sure how well she can control herself.