That's where you're wrong. The chameleon can hide but it's going to try to attack her and her AOE can kill it. Katsuya can catch the bird when it swoops down to attack as it so does. And Katsuya can immobilize cerberus.Sakura has no way to detect the chameleon, catch the bird, or neutralize the Cerberus. Therefore Animal Path still wins.
None of the animals can hurt katsuya so it's not a big deal.
You forget she can have a smaller katsuya on her shoulder that she can make bigger at will. It will spray the toungue of the chameleon and kuchiyose will vanish.The chameleon is the only one really necessary. Animal Path hides inside his chameleon, then the chameleon sneaks up behind Sakura and entangles her with its tongue. Animal Path jumps out of the chamaelons mouth then stabs her with black rods. GG. If needed, Animal Path can summon cerberus to distract her while chamaelon sneaks up.
Byakugou >> black rod Sakura tanks it and punches his lights out.