From early on in the RPG, the Battle of Four Island. Not only did it signify the end of the first major arc of the game—firmly establishing the conflict between Team Liberty and Team Rocket—but it was also the first all-RPG-encompassing battles in the game. Naturally, there were a lot of awesome moments included within.
Bluefalcon's Last Stand against the invading Rocket forces, specifically the group led by Ortrune. Even though she ultimately failed in stopping them from stealing Team Liberty's database of Agents, it was still really cool.
Many of the PC-vs-PC battles across the Alamo and the beach.
The destruction of Team Rocket's airship—as well as the fact that they even had such a thing to begin with.
The Dismantling of Soil Colossus, Inc. is full of awesome. Just to name a few:
The initial attack on SCI's base, in which Team Rocket's strike team—consisting of, at most, thirty agents, including Surge, Koga, Sabrina, Lafoyae Belrose, Shadow Admin Buzz, and Shadow Admin Slight himself—effortlessly disable power in virtually the entire base, simultaneously mowing down any SCI agents they come across.
Koga pulling an Ezio on Nemo Buck, after using a combination of explosions, diversions, and poisons to clear out a hall full of gun-wielding guards.
Shadow AdminSleight blasting down a door designed to survive nuclear explosions using only his Magmortar, before proceeding to demonstrate a ridiculous amount of heat tolerance—meaning, Sleight was more or less unaffected while Buzz and Surge had to cover their faces and use a Tyranitar to block the heat. The physics-defying-ness of this was even lampshaded by his target and Sleight himself.
The makeshift Meteor Mash used against pseudo-Groudon in Sootopolis. Specifically, a Meteor Mash constructed using the remains of the buildings that the pseudo-Groudon had destroyed earlier, and which dealt quite a bit of damage. Hoist by His Own Petard, indeed.
Esen's battle abilities. She effortlessly trounced Victoire despite the latter's team being fully capable of taking out her much-frailer Flying-Types. And in her first appearance, she managed to do the same against Sabrina, Koga, and Lt. Surge until Team Liberty interfered and threw off her game.
Lachina's introduction, with dozens of Pokémon Rangers descending from helicopters to assist in cleaning up the destroyed Sootopolis City.
Basically any major, plot-relevant battle, but the events in Castelia City, in particular, were this Up to Eleven. Especially since it signified some of the first major, human-caused devastation in the game, with long-lasting impact on several of the characters involved.