The moment at which a character realizes that things are finally starting to go their way when they're in danger. Perhaps it seemed that the only option was a One Way Trip or a Heroic Sacrifice, but suddenly The Cavalry appears on the horizon. They might not say anything in particular, but the look on their face is priceless.
The effectiveness of this moment can be affected by their change in confidence. An arrogant, so far unbeatable supervillain suddenly realizing he's got the ace in the hole he'd been hoping for is difficult to make this trope work with, but a downtrodden hero or Ineffectual Sympathetic Villain who has faced hellish adversity at every turn can usually pull it off with little difficulty.
Basically the Inverted Trope of Oh Crap. It can often be an Oh Crap moment for the opponents of the character having a Hell Yes Moment.
Some situations where this commonly occurs:
In Attack on Titan, pretty much anytime Eren shows up in Titan form. A particularly special case occurs at the end of episode 24, when he shows up and punches the Female Titan right in her face, after suffering a humiliating defeat during their first fight in episode 21.
Much earlier in the series, Rossiu has one as Simon shows up for his epic He's Back moment.
In Maiden Rose, Klaus has one of these moments during the night training exercise at Luckenwalde. Early on Taki is knocked unconcious and Klaus carries him away from the combat, his trauma from losing his former comrades surfacing as he just waits for Taki to wake up. When Taki finally comes to he acts cold and aloof as usual and they go over how bad their situation is, made worse when they hear the barking of dogs. Then Taki stands up, pulls out his knife, and the following conversation ensues:
Taki: "Klaus von Wolfstadt, I ask you to join me."
Klaus: "There we go."
In Chapter 698 of One Piece, just when everything looks like it's going to end horribly, Former Admiral Kuzan, also known as Aokiji the Blue Pheasant, shows up to put a stop to the beatdown Doflamingo has been laying on Smoker.
The Straw Hats themselves are prone to causing this. Nearly every time a major villain is beating someone up, one of them, nearly always Luffy, turns it around with a Crowning Moment of Awesome.
The most awesome by far has to go to Usopp/Sogeking in Enies Lobby: despite the crew's best efforts, Robin was about to be dragged through the Gate of Justice by Spandam, and therefore lost forever, and their main hope of stopping this, Franky, had just apparently been blown up by a landmine. And then out of nowhere, Spandam is shot. Cue Sogeking standing atop the tower of justice, singing his theme tune as he shoots down everyone near Robin, at a range that no gun could reach, and Franky walking out of the smoke to pick Robin up.
During the Marineford arc, Whitebeard joins the battle. TREMENDOUS amounts of awesomeness and butt-kicking ensue.
Bleach: When Charlotte is about to defeat Yumichika, he explains that his Finishing Move will kill Yumichika inside a barrier that cuts him off so completely from the outside world that none of his friends and allies will be able to know he's died. Unfortunately for Charlotte, he had no idea that Yumichika was hiding a Coverblowing Superpower that he had been refusing to use because he didn't want his friends and allies to know he possessed it. For a moment there's an incredible expression of raw disbelief on Yumichika's face before his gentle "thank you" reveals Charlotte has just handed him the fight on a silver platter. The Anime milks this moment even more by adding in a Dramatic Pause and Glowing Eyes of Doom as well.
Waylander has this reaction in Jason X when he sees the upgraded android KM-14 about to fight Jason Voorhees.
Sky High: Layla won't use her powers except in self-defense. One of the villains, believing their side has already won and that Layla's a wimp anyway, attacks her just to be petty. "Big. Mistake." Also counts as a Let's Get Dangerous moment.
The Lord of the Rings: Plenty of them. When Gandalf and Éomer arrive at Helm's deep, both Aragorn and Théoden make those. When The Rohirrim arrive on the Pelennor fields, Gandalf makes it. When Sauron explodes, All the fellowship makes it.
The ending of Ink gets two of these: when Ink realizes who he is and delivers an enormous can of whoopass and when enough Storytellers show up to drive off the attacking Incubi from the hospital.
In Last Action Hero, Danny has one of these when Whitney escapes her captors and pulls a gun on the guys holding him. Everyone notices.
The Fifth cohort after Percy, Hazel, and Frank storm the defenders’ fortress during the war games. The entire legion, especially Reyna, when they pull a Big Damn Heroes during the invasion. Not to mention "TWELFTH LEGION FULMINATA!"
Frank taking charge of a ghostly Roman army in the House of Hades after an emergency promotion to freaking praetor.
Nico: "Now that's more like it. Let's turn this tide!"
In The Return of the King, when Aragorn's banner unfurls over the corsairs, it triggers a simultaneous Hell Yes Moment from the defenders of Gondor and an Oh Crap from Sauron's forces.
"And the mirth of the Rohirrim was a torrent of laughter and a flashing of swords, and the joy and wonder of the city was a music of trumpets and a ringing of bells. But the hosts of Mordor were seized with bewilderment...and a black dread fell upon them."
This happens in Animorphs #45, when Marco is fighting aliens who look like a cross between Cthulhu and razor blades, giving us this priceless quote:
Marco (Narrating): They had exactly one second to think I was insane. Gigantic paws, armed with claws that can gut a salmon before you could say "lox" knocked their heads together.
Rachel then proceeds to Curb Stomp the Hork-Bajir.
In Owl Knight of The Heralds of Valdemar, Darian and his companions are up against a snow-drake when heading northwest to find his parents. Things seem impossible, until Healer Keisha fires an arrow hitting it at the right spot. To Darian's amazement, Keisha runs right up to face the snow-drake, followed by younger sister Herald Shandi who shouts the Trope expression.
The Dresden Files has a ton of these. The most powerful being when it turns out Harry is less alone than he (or sometimes just the reader) thought. Some particularly notable ones:
At the end of Turn Coat, it looks like Harry and his dog are standing alone against the council's inertia, and then Ancient Mai, who has tried to kill Harry twice before, stands up and exclaims "That is a Foo dog." And the balance shifts.
At the darkest moment in Changes, when Harry's back is broken and his apartment building is on fire, his landlady calls out "God help us!" and Sanya comes running around the corner as naturally as if he'd been in the book before that scene.
The entire climactic battle of Changes is a series of these, starting when Murphy pulls out Fidelacchius and spouts an Archangel-fueled, then continuing with the arrival of the Grey Council, and then when they in turn bring Kenku in as back-up. And it ends on a subversion—Harry's inner monologue is going Hell Yes when he sees Martin coming up behind the Red King, only for it to be reversed when Martin reveals he was The Mole.
In the Babylon 5 episode "Severed Dreams": as seen here, after multiple Oh Crap moments, the bridge crew collapses in relief when they realize the third assault force attacking them is actually on their side.
Hamilton: "Let me make this as clear as I can. You cannot defeat me. I am part of them, the Wolf, the Ram, and the Hart. Their strength flows through my veins! My blood is filled with their ancient power!"
And just now, in the 50th Anniversary episode "The Day of the Doctor" comes probably his biggest "Hell Yes!" moment yet, when he turned his deepest shame into his biggest triumphand his brightest hope for the future: making his home planet vanish into a random dimension before the Daleks can destroy it, causing the Daleks to destroy themselves. Not only does he know his homeworld is still out there somewehre but history is none the wiser!
Aquerna's combat final in the Whateley Universe. She's outclassed by a brutal opponent who is not only more powerful than her, but who gets stronger the more punishment he takes. Aquerna's only power is a connection to squirrels (squirrel speed, squirrel strength, talking to squirrels - she's a campus joke). And then she finds the testers have put a big park in the middle of the battlezone. A park full of squirrels.
The ending of the "Crushed" arc in Worm. Behemoth has shrugged off every hit that the heroes have delivered, even after they've done more damage to him in the past few hours than in twenty years of fighting him. Then Chevalier wakes up in the hospital, grabs his sword, and charges Behemoth, even though he's still recovering from major surgery. Chevalier's Heroic Sacrifice is able to force Behemoth to retreat back underground, having come closer to killing him than anyone else in history...and then Scion finally shows up, drags Behemoth out of the ground, and vaporizes what's left of him, finally managing to kill one of the Endbringers.
The Order of the Stick: The Order is about to get finished off by Tarquin and his surviving Kingdom Of Blood cohorts (Except for Elan, whom Tarquin wants to level up for an epic confrontation). He's interrupted by an airship showing up and Elan's cries of "Look! Roy, it worked! It worked!" note The airship belonged to Elan's mentor/"good" father figure, Julio Scoundrel, who Elan convinced to come back them up.
The first season finale of X-Men had this with the team fighting a losing battle against "THOUSANDS of Sentinels!", and Professor Xavier's jet crashing to what looked like a fiery death... only to stop falling a foot above the ground and be righted by a magnetic field.
Magneto: Did you think I would let you die alone, Xavier?