Katara defeating Zuko in a sparring match early on in Not Stalking Zuko by tickling him. Not only is it a nice display of her Combat Pragmatist nature, but it also shows that the stalker diary served one of its original purposes- finding Zuko's weaknesses.
Katara using bloodbending to save Zuko's life in Not Stalking Zuko. As well as heartwarming
Katara's speech to the Water Tribe men. Sure, it did very little but it was still an epic moment.
Like the show Katara vs Azula, but particularly this line:
I'm from the watertribe. I know all about knots. She won't be moving for a long time. The fight with her was over.
Katara intimidating The Hippo to back off, after Toph tried to escape Katara cleaning her by siccing The Hippo on her.
Zuko's speech in Chapter 11 of Not Stalking Firelord Zuko, in which he denounces the war as self-destructive, and makes it clear that he wants peace. It's the first time it becomes apparent that he can really handle the job.
Hakoda meeting Jet for the first time and quickly putting him in his place, demanding to be called "Sir Hakoda."