Anime/TheVisionOfEscaflowne, being a mecha series with lots of action as well as development, has several of these.

* Van getting a quick crash course in psychic powers, then proceeding to walk straight into an ambush set by entirety of Dilandau's elite bishonen squad, and hacking through them at a rate of roughly one per second, despite them being invisible, while their omnicidal psychopath leader more or less goes catatonic.
** For that matter, Balgus parrying blows from a Guymelef on foot, with his opponent and both of the involved swords being a few times his size.
** The scene near the end where [[spoiler:Van dumps Escaflowne, which refuses to stop the killing, and to go save Hitomi, and sprouts his own wings to fly to her]].
** One could argue that his first appearance is a Crowning Moment; the [[PintSizedPowerhouse skinny short kid]] kills a dragon with nothing but a [[KatanasAreJustBetter katana]], a shield and a breastplate -- and the katana's all he has left at the end.
* Hitomi Kanzaki running through half an Astorian city wearing a fancy gown, ripping her long skirt when it gets in the way and managing to tackle Van to the ground to save him from a surprise attack from Dilandau.
** Earlier, she long-jumped over eight-to-nine feet of space between the airship and the floating fortress despite Merle's cries of "You'll never make it!".
** And when ''everything'' comes crashing after Hitomi tried to use her tarot readings to [[spoiler: make sure Millerna would marry Dryden instead of running away with Allen, whom Hitomi also loves]], what does Hitomi do? Instead of going into an HeroicBSOD, Hitomi [[spoiler: briefly explains to Millerna what was going on, then thinks "What am I doing? I've got to go already" and, as Naria and Eriya demand to have the "girl from the Phantom moon" handed over, she bravely goes to them and yells "I'M THE GIRL FROM THE PHANTOM MOON! GO AND TAKE ME AWAY ALREADY!" ]] For an OrdinaryHighSchoolStudent who's got no ActionGirl skills, Hitomi demonstrates ''lots'' of guts.
* [[TheMedic Princess Millerna]] working her ass off to save Allen's life and pretty much bring him back from the dead. Since this is a Medic who's NOT a WhiteMagicianGirl and was using ''a very old manual as a guide'' as she raced against the clock... wow.
* Merle gets her own moment when [[spoiler: she fearlessly stands up for Van in front of the CatGirl twins Naria and Eriya, shielding him and yelling at them to leave Van alone. ''And they do'', reminded of how similar they were to Merle when they were children.]]
* Also, how Folken Lacour de Fanel ''finally'' [[spoiler: reconciled himself with his brother Van]]? By [[spoiler: saving Van from a ''huge'' dragon that was tracking both of them when they were disarmed and without any Guymelef they could use to fight it. Van was pretty much pissing in his pants from fear ([[NightmareFuel and with GOOD reason]]), but Folken manages to calm him down and get both of them to safety.]]