Despite being off-duty, Adam Jensen takes down a ten-Asari bank robbery single-handedly through stealth, offers himself to the last one in exchange for her hostage, then defeats her non-lethally but painfully when she still refuses to see the light.
The first onscreen appearance of Johann Liebert Ramsus has him concoct a brilliant, bloodsoaked plan to get out of his holding facility, showing both his mental and combat prowess in the process.
Ace Combat The Equestrian War rightfully introduces Mobius as a One Pony Army. He dispatches three griffon soldiers, each with a single hit and even stares down Razor. The entire Mirage squadron, especially Rainbow Dash, watches in awe as he performs his feats. By the end of the chapter, it is revealed he is a living legend and the best pegasus flier in the world.
Claymade's sequel to The Dark Lords Of Nerima introduces the new Big Bad by having him casually defeating an assassin trying to kill him (that he had hired himself), who had already easily torn through his security forces.
Like in canon, Erika insults Miho, claims Oarai should not even be entering the tournament if it can't hope to win, and gets offended when Mako (Reizei) brings up the possibility of them being defeated.
Maho, seeing Miho in the cafe, is forced to conceal her emotions and choose her words carefully as Nishizumi heiress. The only thing she can bring herself to say is "I didn't think you'd still be doing tankery" After seeing that this answer upsets Miho, she thinks, "Forgive me, Miho...". She subconsciously agrees with Hisa's arguing that one should not lose sight of one's reasons for wanting to win, and as she walks off, hopes Miho is happier at Oarai.
Teru, in response to Erika derisively bringing up Hisa's being a no-show at the middle school tankery tournament three years ago, tells her, "Some people have parts of their past that they don't want to talk about." When Saki notices her and calls out to her, asking why she is denying having a sister, Teru freezes in surprise before walking off without saying anything to Saki.
The first lines introducing Kaji in the Honor Trip Arcos Special Chapter have him scowling, & annoyed at having to wait. The next paragraph is a flashback detailing the brutalNo-Holds-Barred Beatdown he gave to a fellow soldier. Similarly, the other Arcosians are introduced in ways that reflect their personalities.
In The Wizard In The Shadows, Harry introduces himself by chasing off the Nazgul at Weathertop with a patronus, setting one on fire, and then, a little later on, when asked what he's doing by a thoroughly suspicious Merry, says a line that cements him as a Deadpan SnarkerHurting Hero and a total Badass:
"Looking for trouble."
In Prince Of The Dark Kingdom the first thing Voldemort gets to do on-screen is to crucio an 11 year old Harry for something, that technically wasn't his fault and usually would have warranted a laugh, instead of a curse...
Sunny Breeze, the protagonist of Racer and the Geek is introduced all alone on a Friday night, when he is drunk, working on a conlang, and keeping an FN FAL within easy reach.
In The Non-Bronyverse, TD's establishing moment is when he walks up with quiet dignity and grace and punches Celestia in the snout.
If the Apple Trust from the Lunaverse was not meant to be seen as unsympathetic, neigh (sic), villainous, the self-righteous and jealously monopolising ways they first showed up in Boast Busted and Longest Night, Longest Day did not help.