Catwoman makes her debut in style. She runs circles around Batman during their chase scene, while casually flirting with him and claiming this is just their first "date". When she finally stops running and actually fights him it only takes her a few seconds to beat him by pouncing at him, sending them both off the roof of a building, and while he crashes down she lands on her feet.
She is also the only villain that Batman was never able to capture for the entire series. He might have been able to stop her heists but he was never able to bring her in.
In "Bird of Prey," Penguin gets the drop on the Batman, ties him up, and actually begins to pull his cowl off, coming within an inch of revealing his Secret Identity—on camera, no less.
What stops him? Alfred, who is tied up nearby, manages to pull himself free and smashes a chair over Penguin's head. He even pulls out a one-liner to go with it.
Alfred: That's for ruining my roast!
Batman reversing Joker's Mind Rape with his own brand of it in the episode "Strange Minds".
Barbara figures out Batman's secret identity in her second appearance using an approach similar to the Awesomeness by Analysis D.A.V.E. would later employ in the season finale. While she's convinced otherwise by the end of the episode, it's only because Bruce himself doesn't remember that he's Batman at the time.
Just anything D.A.V.E. does in "Gotham's Ultimate Criminal Mastermind".
D.A.V.E., "Gotham's Ultimate Criminal Mastermind", a robot with the composite mind of Gotham's worst criminals. After he builds a new body, he quite casually uses a laptop to steal all the money in every account in the city (or as he puts it "I'm rich, you're not!"), blacks out all of the power except his name on every screen, then notices that Batman is right behind him and defeats him.
However, Batman turns this around on him in his own Moment of Awesome when he points out that D.A.V.E doesn't have an origin, all the ones he lists are of the criminals he's made up of. This leads D.A.V.E. into having a Villainous Breakdown, leaving himself open for a finishing blow.
Harlene, before becoming Harley, ordering two hyenas that Joker sics on her to sit. And they do it.
The Joker's debut was really good, especially with his one liner:
Guard: Cell 223 vacant... (turns around) Guard: What the? Joker: I was feeling a bit screw-loose, so I... checked myself in. Guard: Who... who are you? Joker:My Card. [laughs evilly]
Joker: What are you gonna do? Lock me in the loony bin? I'm already here!
Bane get a villainous one when he curbstomps Batman in their first fight.
Curbstomp? He utterly beat him into the ground, breaking several of his bones and handing Batman one of the worst defeats he had in the entire series. All well delivering a few good Badass Boasts. Shame he had to suffer such a massive Villain Decay.
Batman gets his own in his second bout with Bane. He stabs Bane's wrist with a cable, disabling his Venom supply and knocking him out cold.
In "Brawn", during a circus performance, a muscleman is continually upstaged by a clown-muscleman who keeps trying to imitate his act. After having enough of this, the muscleman back-hands his smaller clown counterpart. But, if you didn't see through the Paper-Thin Disguise before, this clown is none other than the Joker! When he makes his reveal, he gives the muscleman a real stink eye. And not just any stink eye, this is the same "Just who do you think you're dealing with" stink eye he gave to a guy who road-raged him in "Batman the Animated Series" note Episode "Joker's Favor", effectively intimidating him. And this Joker manages to execute that same level of intimidation in a muscleman.
Joker: (with mock approval) Ooh! Tough guy!
Penguins martial arts skills. He can launch himself 20 feet in the air and complete on a full split.
Can we call "Thunder" Batgirl's Crowning Episode of Awesome? She sneaks onto New Olympus without being detected, disables its Thunderstorm weapon before they're able to use it on a bridge full of fleeing citizens, and steals one of its most important components just in time to stop them from shooting down Batman. Then, when Batman gets captured, she hacks into their system in order to hold it hostage and buy him time to escape. When Maxie Zeus finally catches up with her, she smashes the vital component she stole earlier to stop him from getting it back. Finally, she steers the crash-landing New Olympus into the harbor, minimizing collateral damage like whoa, while everyone else abandons ship. Damn. It really shows how far she's come since her earlier episodes where she screwed up just as much as she helped. Even Bruce is impressed; it's the episode where he finally starts taking her seriously, and he even gives her a set of Bat-Gear to replace her entirely homemade arsenal, saying she's "earned her wings".
In Batman's second fight with Poison Ivy, she shows off her huge arsenal of evil vines and giant Venus Fly Traps. How does Batman respond? Chainsaw gauntlets.
"The Breakout". Batgirl and Robin get credit for holding off Black Mask's minions, but Black Mask takes home the pot in ensuring that all of his minions were highly trained and armed with high-tech weapons and armor. They even took down the Batman and removed his belt!
Superman and Batman taking down Lex Luthor's Humongous Mecha in "The Batman/Superman Story".
Commissioner Gordon in "Night and the City" for doing something fans have been wanting to see for the first two seasons and finally putting Chief Rojas in his place after all the jackass and dumbass things Rojas has done, by ordering Rojas to let Batman go, and release and reinstate Yin after Rojas used her as a hostage.
Hell, the climax in general. Batman defeats three of his greatest rogues with only minor tech support from Detective Yin, who then replaces the Riddler question marks littering the city's skyline with Bat-Signals, showing all of Gotham who really rules the night.
In "A Matter of Family", when Tony Zucco tries to get protection money out of the Graysons, Dick reveals he made a call to the police 5 minutes ago after his monologue, revealing that he was smart enough to get police there as soon as possible. That shows he has what it takes to become Robin in this universe.
The episode "Artifacts". It's 3027, Batman is long dead, along with nearly every character of the series, with one exception: Mr. Freeze. Having preserved himself cryogenically, Freeze is running rampant in a world with no means of stopping him. A handful of detectives unearth the remains of the Batcave, hoping to discover the secret to his defeat, but to no avail, as the data of Batman's computer system has long since degraded beyond use. That is, until one of the detectives notices that the entire cave has 1's and 0's chiseled all over its metal interior. Once scanned, the binary code is translated and reveals a recording left behind by Batman, along with all of his data. That's right, Batman predicted that there would be a day when he was gone, but his expertise would be needed again.
Batman: Welcome. If you're viewing this message, I can only assume one thing. The mission isn't over.
By the end, the group has formed a kind of crime fighting alliance, based out of the Batcave, and have defeated Mr. Freeze using the information Batman left behind. They build a statue in tribute of their founder in the middle of the cave, and take over his role as protectors of Gotham.
Freeze: But I waited a thousand years!! You can't still be here!!
New!Batman: And yet I am here. And always will be here to stop you Freeze. Always!
The 2027 flashback. Batman is middle-aged and very banged up, Batgirl is now Oracle and wheelchair bound, Robin is now Nightwing and apparently not taken seriously. Freeze? He's more powerful than ever. He successfully crashes a cargo plane and steals a rare diamond to complete a device that will put Gotham in an Endless Winter. Batman and Nightwing are frozen solid, Freeze activates the machine. All is lost right? Wrong. Batman programs the Batwing to fire missiles at him to both disable the device and break the ice! Not only that, but what he says once freed is fucking amazing.
Batman (sinister grin): Thanks for the ice pack, Freeze. All you did was numb the pain.
He then proceeds to give Freeze a walloping, uses the diamond to pierce his suit, injects him with an anti-freezing serum, then crashes the Batwing into him. Even in old age, Batman is still Batman.
In "The Joining", the supercriminals are helping the police fight off the aliens. When one of the cops asks Gordon what to do when he notices Mr. Freeze, Gordon immediately replies with "BACK HIM UP!"
Then after helping Freeze take out a robot, Gordon and Freeze just nod to each other in respect.
Francis Gray singlehandedly defeating Batman, Robin, and Batgirl in "Seconds" by using his "Groundhog Day" Loop powers to predict their moves. If not for Batman locating his son Matthew in time, his plan to gas Gotham would have succeeded.
Alfred shoots Dracula with a crossbow. It doesn't work, but it's the thought that counts.
Batman seemingly cornered by Dracula in the Batcave, only to switch on the sunlight-storing/releasing machine he was building, shining a blinding light toward Dracula with only Batman's shadow keeping him from death. This scares the crap out of Dracula, who realizes that he's Bruce Wayne. He responds (how else) "I'm the Batman. And you're dust". Then he uses his grappling hook to get out of the way, burning Dracula alive until he's so brittle when Batman delivers a kick it smashes him apart, sending ash and bone everywhere.