it's why Zuko for once ACTUALLY had a chance to beat her in a straight fight, she was 'slipping'.

The music at the start of that final Agni Kai is sublime.

https://www.youtube.com/watch?v=Ae9VB_Cf5RM

Also for anyone who was paying attention throughout the series you can see just how much control Azula has lost since her first appearances, going from precise two-finger points when firebending to entire fist thrusts. She was an obvious prodigy as seen when her flames turned blue but still ended up losing to both herself and her brother who in the end took firebending to a completely new level by combining his existing skills with the knowledge from both the progenitors of firebending, the dragons, as well as what his uncle taught him who developed novel techniques observing other bending schools. How he moves his body during the Agni Kai highlights this with his fluid movements, like waterbending, his deflections of incoming attacks, like airbending, and then during his own push the unrelenting force behind his attacks, like earthbending.

Also you can't forget,

RUFIO!