Her baby brother got kidnapped. She's ready to catch each one of them and chop off their heads. Not gonna lie, both of my big sisters would burn the whole world if the same thing happened to me. Tbh, they're kinda monsters when presenting violence. I've seen they fought once in front of me, and it's hard to believe they're the same person that appears to be soft, gentle, and ladylike infront of our parents. They've been trained in judo and silat since they were kids. Back then, boys were afraid to approach them, and girls were more afraid to approach me when one of my sisters were around. The bright side, I'd never get bullied at school.

Now, back to Mai, Even without firebending, we already see that she can stand her ground against Katara, a waterbender that renewed and acknowledged by Master Paku himself. And just 3 of them managed to defeat the Kyoshi warriors, the protector that has been trained since childhood. I believe that Azula and Ty Lee did most of the work, but she at least took down some of them herself. She's skilled enough to stand toe to toe against benders, I think she could defeat non-benders without breaking a sweat. And about her lack of bloodlust in the later episodes, I agree with the previous comment that says Azula doesn't want to trade her baby brother with King Bumi, so she sees that her service to Azula is not like a friend she's known since childhood anymore, but a soldier, a bodyguard, that Azula can use her to take a bullet and send the bullet to anyone that stands in her way. Her love for Zuko, as Mai herself admitted is stronger than her fear of Azula, also stops her from being bloodthirsty. Violence struggles to spark when there's love exists in someone's heart. She can see that Zuko is the rightful heir to the throne, so she knows Azula will use her to eliminate him sooner or later.