Chaotic Evil for Ayallah.
"A chaotic evil character does whatever his greed, hatred, and lust for destruction drive him to do. He is hot-tempered, vicious, arbitrarily violent, and unpredictable."
"Here are some possible adjectives describing chaotic evil characters: violent, cruel, capricious, malicious, untrustworthy, unreliable, heartless, volatile, inconsistent, uncaring, unfeeling, deceitful, discourteous, selfish."
Her big goal, as I have seen, is perfection of the self--namely, through battle. She cares nothing for killing other people, and only seems to care about allies so far as they are means for her to get more combat, and test herself against more people. Once they are no longer useful for that then she moves on to someone else who can.
Strength is what is important to Ayallah. She respects people who are skilled and capable, and dismisses people who are not.
At best, she might be Neutral Evil. But I haven't really seen anything to make me believe she really cares about authority beyond their ability to fulfill her need for destruction.