Eric's extraction at the start of the first episode is an excellent Establishing Character Moment for the Principal Team. There's Ange cleverly using her Cavorite device for both mobility and offense, Chise disabling a speeding car by slicing its wheel with her sword, and their escape in Dorothy's veryCool Car.
Say what you will about Normandy's men, but when Chise holds one of them hostage, none of them are afraid to gun him down in an attempt to get her as well. Too bad for them that Chise is skilled enough to effortlessly cut them all down anyways.
Ange seamlessly impersonating Princess Charlotte and tricking Morgan into handing her the vault key. Not to mention tricking her own superiors into accepting Princess Charlotte as a member of her team.
Beatrice realizing her Voice Changeling abilities to help Ange, in spite of both not wanting to help the Commonwealth spies and considering her mechanical larynx a curse and shame up to that point. She acts quickly and doesn't look back, and no one suggests it to her.
The team assaulting a ship and eliminating nearly an entire platoon of guards effortlessly. They even go above and beyond their original mission of capturing the Kingdom's C-ball prototype by securing the C-ball AND capturing the entire research team that built it.
The whole action sequences in episode 5, especially the sword duel between Chise and her father Jubei Todo.
In Episode 7, Princess decides that simply purchasing the laundry mill isn't enough to ensure completion of the mission: she will turn it into a profitable enterprise that is also safe for its workers. With the machines rearranged and conditions improved, profit margins are increased by over 200%.
Further, the laundry mill now gives Princess a source of income with fanatically loyal employees, completely independent of royal largesse. An official tweet suggests it will make the equivalent of 10,000,000 yen per year in profit for the Princess. Her own goals of gaining political power were improved by this move.
Ange is a young pickpocket, trapped in the role of Princess Charlotte after they were separated during the rebellion. She is in the middle of a web of intrigue and politics, and a single misstep will mean death. The new Charlotte plays the role flawlessly, mastering the abilities to an extent that the new Ange never did or could have to hear it from her. And on top of that, both Ange and Charlotte have taken to their roles so well that even by the end of the series, no one, not even the greatest spymasters in the Kingdom or the Commonwealth has even the slightest suspicion as to their former identities.
When Chise duels a Smug Snake nobleman with pistols, hers fails to go off properly. When the nobleman taunts her with her inability to prove that the gun was tampered with, she doesn't react when his bullet almost clips her face, then uses her ribbon as a sling to wound him in the shoulder.
The girls have to cross a yard full of guard dogs in episode 10, so Beatrice alters her mechanical larynx to an ultrasonic pitch that puts the dogs to sleep.
"Floor it."
Team White Pigeon abandons all attempts at covertness and makes an all-out charge to the Cathedral to save Princess and stop the assassination.
Crown Handler, Part 2, has several moments.
The unnamed assassin who killed Winston takes on both Ange and Chise in close quarters and bests them. Granted, no one is killed in the exchange, but he almost takes out the three combat-worthy members of Team White Pigeon singlehandedly.
When Ange, Chise and Dorothy capture a suspect in the case, he calmly waits until one of his lackeys attacks them with a steam-powered dragon stage prop, complete with flamethrowers. The suspect uses the opportunity to flee, but Dorothy downs him with a long-range pistol shot to his leg.
When Ange and Chise find one of the Cavorite bombs is on a ship that has Princess, Beatrice, Mary, and hundreds of politicians onboard, Ange manages to neutralize the bomb by connecting a fire hose to it and then using the hose to pull the bomb into the ship's machinery, crushing and disarming it seconds before it would explode.
