Jayce's first battle as an Espurr. Despite only being a Pokemon for a few minutes and knowing next to nothing on how to use Pokemon abilities, he still manages to fend off a Mismagius while protecting Trustful Grace and Rock Soup, even going so far as evolving into Meowstic through sheer determination to protect. Fridge Brilliance sets in when you note that canonically, male Meowstic excel at defensive and supportive moves, so it makes sense that the trigger to evolve for a male Espurr is the want to protect.
The Shiny Charizard's Big Damn Hero moment when he saves Rainbow Dash and the Wheezing. Made even more awesome later when its revealed that the Shiny Charizard is Red, as in the hero of Pokemon Red, the game that started the entire franchise. Word of God states that the choice of Pokemon form (a Shiny Charizard) was a tribute to Red being the very first hero of the Pokemon series, and therefore gave him the form of the very first iconic Pokemon.
Seth deserves a mention for the bit in his first chapter where he shuts down a confrontation at the Nimbasa Pokemon Centre with a trainer who is repulsed by him being a supposed Pokephile (he isn't, though he does publicly support Human-Pokemon relationships on the basis that Pokemon are sapient creatures). He calls out the trainer for his profanity, pointing out that there are children present, and tells him that he can settle this like a trainer if he wants to. What's really awesome about this is that Seth says nothing to correct the trainer's assertions about him, thus sidestepping the potential implication that actual Pokemon lovers would be any more deserving of the abuse.
Another Seth moment is when he finally meets Arceus. He attacks Arceus, and gets away with it, with Arceus acknowledging how he didn't think things through all the way.
Naruto and Carapace's fight against the Blastoise counts, with all three getting points for various parts of the fight.
When Solana and Lunick approach Twilight for help in apprehending Gene, she proceeds to effortlessly deconstruct the reasoning behind anti-Pokephilia laws while waking the two up to their years of indoctrination, just by asking a few questions.
A few chapters later, Twilight has the same argument with Professor Hastings, after he tries to convince her to enact segregation between former humans and natural-born Pokemon, to prevent "cross-breeding". After Hastings proves much less open to convincing than his subordinates, Twilight shuts him down with the following:
Twilight: Dont. I dont doubt that some of those people deserved what they got. That some of them were actually... using their Pokémon, that some were horrible people. But not all of them are like that. Gene and Belle are happy together, Falkner and Pidgeot are happy together, and Im sure dozens of other humans are happy with their Pokémon partners. And Im certain that they deserve to be happy, so no. I will not help you.
This is followed by Hastings trying to get Solana and Lunick back on his side. Lunick responds by kissing Solana and retorting, "Shes a Medicham, and shes a human. Im a Hitmontop, and Im a human. What does that make us now?"
You gotta give Weiss credit, when Victoria stabbed him right through the hand to mark him for messenger fire. He keeps his composure despite having just been stabbed through the frickin' hand.
Seth and his team taking down Koga when he attempts to sneak into Ponyville to capture Gene.