"Tali, Nihlus wouldn’t drag you across half the galaxy if you weren’t up to this. You introduced yourself to us by throwing a grenade at a crooked info-broker!"
The first onscreen appearance of Johann Liebert Ramsus in Mass Effect Human Revolution 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.
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.