In one episode, Aquaman and Atom are in the middle of a Fantastic Voyage through Batman's body. While escaping from deadly nanobots, Aquaman tries to use his fish telepathy to communicate with a blood cell. Atom questions Aquaman's sanity and says there is no way it will work. It does.
How about the end of "Day of the Dark Knight!"? Batman and Green Arrow are facing down Morgan Le Fey, who has Scaled Up into a dragon form in an attempt to fry them before the "one who is worthy" can draw Excalibur. The two of them work together to draw Excalibur and Batman passes Excalibur to Green Arrow, who fires it like an arrow at Morgan! And it works!
The end of the first part of the two-part alternate universe story, where Red Hood blows Silver Cyclone's (robotic) head offin the middle of his dramatic evil monologue!
From the same episode and character (though much more low-key) the flashback of Red Hood's origin story where he destroys the mirror. With that one act, he overcame what his counterpart the Joker never could, and became more than he could ever hope to be.
This exchange, as several Injustice Syndicate members realize they've failed to kill their "Owlman imposter":
Blue Bowman: Who is this guy?! (He, Scarlet Scarab and Dyna-Mite are easily KO'ed) Batman: I'm Batman.
The end of the second part of said two-parter. Batman travels through various parallel Earths and teams up with... Batman, Batman, Batman, Batman, Batman, and Batman. This includes a psychic Batman, a cowboy Batman, a pirate Batman, a Batman in Powered Armor, a hulking miscled Batman and a vampire Batman. The seven Batmans then team up to fight an evil Batman and his team of supervillains. Total Batman overload.
Batman, Aquaman and Adam Strange stop a solar-powered superweapon from devastating Rann by using a zeta beam to transport Earth's moon 25 trillion miles and create an eclipse before beaming it right back to prevent the planet from cracking apart!
A slightly smaller one is Aquaman's He's Back moment.
In "Trials of the Demon!", Sherlock Holmes meets Bats and performs a perfectSherlock Scan. Then Batman looks at him and goes "You're Sherlock Holmes". When Holmes wants to know how Batman knows who he is, Bats deadpans "Your hat."
"I was born in flame!"
In the teaser to "Invasion of the Secret Santas!", Batman punches the bowling balls thrown by Sportsmaster. And they shatter.
What about the Green Lantern team up episode, where, Batman takes out Guy Gardner in one frickin' punch, and when, near the end of the episode, Guy Gardner fights Sinestro to SAVE THE LIFE OF A PLANET.
Also in this episode, we have Hal Jordan going up against the entire Green Lantern Corps (puppeted by Despero the whole time, mind you), and successfully beating them in typicalGL style:
Hal Jordan/Green Lantern:
"In Brightest Day, In Blackest Night, No evil shall escape my sight Let those who worship evil's might Beware my power... GREEN LANTERN'S LIGHT!"
In "The Eyes of Despero", after a magic throwdown ends with the villain knocking off Dr Fate's magic helmet from behind, the villain brags "You are defenseless", and launches into a good evil laugh—only to get cut off by being punched in the face several times by Fate as the musical score shifts gears into awesome. As the villain falls, Fate remarks "Actually, I'd call those boxing lessons I got from Batman a pretty good defense." Nothing like going straight from a Wizard Duel to Good Old Fisticuffs.
In "Night of the Huntress", Batman, Huntress (of course) and a lovestruck Blue Beetle take on Babyface, who has stolen a bunch of impounded Humongous Mecha and is going to take over the various crime families. After bragging about how Batman can't stop him in his new Mech, Batman simply jumps into his Batmobile...which then transforms. It's on now!
No love for the Music Meister? Using only his voice, he eventually brought the entire planet under his hypnotic control, and put on the largest musical ever. Simultaneously.
"Drives Us Bats" is the most Awesome moment of the series — and it's all the Meister's. Think of it — he leads Batman on a cross-city chase, always staying out of reach, making Bats MISS — and snarking on his infallibility all the way! By the end of the song, the entire DC Universe is proclaiming how infuriating Batman can be. All this — and so many costume changes along the way, you lose count of the references.
"Return of the Fearsome Fangs", where the Terrible Trio steal the Wudang Totem with the help of the Shadow Clan (ninjas), to become monstrous humanoid animals, enhancing their already-formidable martial arts abilities. How do Batman and Bronze Tiger beat them? By snatching the Totem, empowering themselves into super-creatures, and having a no-holds barred super-powerful kung-fu brawl with Shark, Fox, and Vulture.
This scene from "Chill of the Night":
Batman: "You are the slinking coward who murdered Thomas and Martha Wayne." Joe Chill: "That was a lifetime ago!" Batman: "Yes, my lifetime. You took them without mercy or regret, and in cold blood, Chill!" Joe Chill: "How do you know this? How could you possibly—" Batman: "I know because I watched it happen. I know because I am the son of the man you murdered. I... am Bruce Wayne!"
A meta example of this is Diedrich Bader's acting in this scene.
Black Adam from "The Power of Shazam!" gets his own Moment Of Awesome by simply being the first villain to completely outclass Batman.
In the same episode, after Dr. Sivana steals the power of Black Adam, Batman tries to attack him, but it didn't work and, while Dr. Sivana is bragging about his powers, Batman said that he was a powerful champion but would never be as strong as the wizard Shamaz. The superpowered Dr. Sivana ammends him, saying "It's SHAZAM!" Guess what happens?
Which is also a shout-out to Black Adam's first (and intended as last) appearance in the comics. Captain Marvel's non-superpowered uncle takes the Batman role, tricking Black Adam into saying "Shazam" and destroying himself, as his human body was too ancient to survive. However, Black Adam either got better or that never happenedanymore.
Firestorm lifting up Captain Marvel so that he can defeat Starro with his magic lightning, possibly a homage to Kingdom Come.
The Birds of Prey working together to escape a watery death in Matches Malone's shark tank, which cumulates with Black Canary bringing down the house. LITERALLY.
Black Canary(looking to Huntress after a well-placed arrow removes the gag from her mouth ). Nice Shot! (smirks) My turn! (destroys shark tank with her Canary Cry).
Another for Bats in "Emperor Joker." After Joker has become a Reality Warper and killed him over and over again, he begs Joker not to take his sanity. Joker promptly screws open Batman's head, crawls into his mindscape, prepares to toss some important-looking documents about...and gets stopped by a voice out of nowhere: Batman himself. Batman explains how disciplined his mind is, and segues it into a speech about how Joker needs Batman in order to exist. This is punctuated by Joker entering a world without Batman, and turning into an ordinary businessman. Joker willingly surrenders his omnipotence in return for his characterizing madness.
How about Joker repeatedly murdering Batman? Sure, he was supercharged by Batmite's powers, but nobody has killed the Batman in so many ways so fast.
In "Bat-Mite Presents: Batman's Strangest Cases!", we get the Scooby-Doo crossover. Bat-Mite lampshades the fact that due to Executive Meddling, Batman couldn't throw a punch back then...and then says that his Reality Warper powers render the whole thing moot, and gives Batman, Robin, Joker, and Penguin the ability to actually fight each other. And then he does the same to Shaggy and Scooby, who proceed to pound the stuffing out of Joker and Penguin. And who gets to KO the Joker? "Weird Al" Yankovic. WITH AN ACCORDION.
The fact that they adapted "Bat Boy and Rubin", from issue 8 of MAD back in 1953, is nothing short of amazing.
The epic battle between Batman and Superman in "The Battle of The Superheroes!"
An eagle-eyed comic book viewer might be able to notice that many of the freeze frames in the fight are taken directly from Batman: The Dark Knight Returns.
Not to mention the clever ruse they put on Lex Luthor near the end of the episode. As they confront him, Lex blasts Batman with a raygun, and pulls a Green Kryptonite ring on Superman. And then Superman grins, grabs the ring, and puts it in a box. Turns out that the two of them switched costumes, so "Batman", AKA Superman, is just fine after the raygun blast, and "Superman", AKA Batman, was immune to the Kryptonite.
Not to say Krypto's role in the fight wasn't awesome. He gets thrown into space and comes down, using the heat of re-entry to send Superman flying.
"The Malicious Mr. Mind": Batman uses his grappling hook to activate a laser cannon that shrinks the titular Big Bad from his One-Winged Angel form back to his normal appearance of a harmless-looking caterpillar. And Batman does this while he's been de-aged to a baby!
Detective Chimp is generally pretty awesome in this show, but in "Gorillas in Our Midst" he routinely beats up SCORES of gorillas that are four times as big as him. But the moment that made this troper's jaw drop was when he punched an oncoming gorilla in the guy and LAUNCHED HIM OVER HIS HEAD.
No love for the end of the episode, when Batman gets turned into a BatGriffon?
"Requiem for a Scarlet Speedster!" a fully animated fight between Barry Allen and Professor Zoom both with their powers increase by other speedsters? after Zoom just took a super fast (though granted not as fast as him) Batman out without much effort... Awesome.