"Return to New York, pt. 3". The "final" showdown with the Shredder. Shred-head and Leonardo both leap, swords drawn. Two seconds after they land, Shredder's head falls off. Mind: blown—that sort of thing just doesn't happen in Saturday morning cartoons! Minutes later, after the end of the episode, Shredder's body stirs, gets up, searches blindly for its head, and picks it up. End episode.
Granted The Reveal takes away the sense of awe and fear factor, but back then we could only assume he was undead or worse. This kind of thing on a freaking 4Kids show was to many of us something we'd never see.
In the same episode, Stockman vs. everyone.
"Same as it Never Was." The whole thing. The fact that they were able to produce and show such a dark and bleak episode packed with character deaths on a saturday morning timeslot hosted by 4Kids is means for a pat on the back. Not to mention Donatello's method of defeating the Shredder counts as his personal Crowning Moment of Awesome as it's arguably the most badass thing he has done or ever will do.
AU/Future April taking out AU/Future Karai... with a rocket launcher!
And if it's not SAiNW, Back to the Sewers seems to be one giant love note to Don's fanbase— particularly "Hacking Stockman" and the finale, "Wedding Bells and Bytes". In the first he got the drop on the Cyber Shredder, fought him one-on-one, and, if memory serves, didn't even get hit once— it's an awesome mix of Beware the Quiet Ones and Papa Wolf tendencies, since Don was fighting to keep his brothers safe. The second seems a bit anticlimactic after that, but it was pretty awesome that he took out the Cyber Shredderwith the sameApplied Phlebotinumthat kicked the arc off. All this from the guy who is, arguably, the Squishy Wizard of the main team.
Savanti Romero, one of the Turtles' more obscure enemies, gets one when he fights the Turtles for the second time, but it's not during or after the battle though, it's before the battle even starts, he basically makes these dinosaur bones into Shredder-esque armor for himself, that's actually pretty awesome.
In the "Notes from the Underground" trilogy, Mikey is wary of Quarry, Stonebiter, and Razorfist. Cue a quiet, but poignant shutting up from Donnie.
Mikey: They're monsters!!
Donnie: Yeah? Well, to some people, so are we.
A rather underrated one, but in "Worlds Collide, pt. 2," Master Splinter, along with April and Casey, infiltrate Bishop's underwater base, where the turtles are being held hostage. After subduing a group of armed guards, April takes one of their guns and gives another one to Casey. She offers one to Splinter. His response?
When Michaelangelo fought Kluh in "Grudge Match", he beat Kluh, which was a good fight to watch, to see the quirkiest character in the group put a beatdown on Kluh, right after Kluh put a beatdown on him, and does Michaelangelo finish Kluh off? No. He pushes Kluh down with a finger, and rightfully claims the title of Battle Nexus champion.
In that same episodes, there are more fighters of the same species almost equally powerful to Kluh who are holding the Daimyo's son hostage. Leonardo defeats four of them by himself without trouble. According to Kluh's shocked father, this simply doesn't happen. Yeah, Leo's just like that.
In keeping with the Michelangelo theme here, the fact that he was able to fend off the Turtlebot in What a Croc a good ten seconds longer than the rest of them is definitely impressive, considering even Leo and Raph lost their bouts in five seconds or less. He's the one to finish it off, too.
The Shredder Strikes Back parts 1 and 2 was a Homage to an original issue of the Mirage Comic series, where Leonardo takes on what amounts to the ENTIRE FOOT CLAN by himself. He spends virtually the entire episode in one long running battle where he faces foe after foe and is never given the chance to recover, culminating in a battle with the Shredder's four elite warriors. That he loses does not actually detract from how awesome it is, especially when in Part 2 we see the same Foot Clan attack the three remaining Turtles and Splinter, and we see that Leo basically did as well against the Foot by himself as his family did working as a team.
And then there's that moment in Part 2. All four turtles are down and the Foot is advancing on them when Casey Goddamn Jones crashes through the window on a motorcycle, promptly disposes of half-a-dozen ninjas, and then starts trash talking the rest.
Bishop vs. everyone fight in the episode "Hun on the Run". Watching Bishop use anything he can get his hands on as a weapon—including his glasses and necktie— is a thing of beauty.
Hun himself was pretty awesome in that episode as well, he busts into Bishop's underground base with a tank-like vehicle and pretty much sends Bishop's Mooks running for their lives, and he puts up a pretty decent fight against Bishop himself.
Basically, after two and a half seasons of slow Villain Decay, Hun now has to fight Bishop, the EDF and the Turtles all at once, or fail the Shredder. He doesn't disappoint.
Leo's finishing off Hun in "The Shredder Strikes". I could try to describe Leo's jump-kicking here, but words wouldn't suffice.
His battle against Raphael was especially memorable and awesome, due to the fact that Mikey never even has to throw a single punch, kick or any attack. Mikey defeats him simply by annoying him into a fit of rage and dodging his attacks, essentially making Raph defeat himself.
The final battle against the Tengu Shredder in the Lost Season. We have almost all characters (including some of the villains) teaming up against the evil forces of the Tengu Shredder. The Shredder and Turtles change into dragons, have a large battle in the skies. And then even the spirit of Hamato Yoshi appears and cuts the shredder IN HALF VERTICALLY! ON A 4KIDS CARTOON! Granted, he wasn't human anymore. But still, his death was one of the few that's explicitly shown.
His appearances may be few, but everytime Miyamoto Usagi from Usagi Yojimbo appeared, he made those episodes count. Special props to both him and Leo when the latter ends up in his world and they fight to save Usagi's friends..
Everything involving Bishop. EVERYTHING. He's probably the most competent non-mystical fighter in the series. Sure, he's got super strength, but that's pretty much it. He goes up against multiple armed ninja masters with his bare hands or an Improvised Weapon and uses skill and pragmatism to come out of the battle with something that benefits him. Plus, who can resist that nice suit of his?
The entire episode of The Christmas Aliens was one huge crowning moment of awesome and heartwarming for Mikey. In a nutshell, some Purple Dragons steal a truck full of toys meant for orphans to make some easy money, Mikey takes them out, hijacks the truck for himself, and uses it to defend himself from more Purple Dragons while simultaneously evading the police who've mistaken him for a Purple Dragon all while keeping his new friend safe, returns home to convince his family and their party guests to move the party to the orphanage and successfully delivers the toys to the orphans. Oh yeah, and he does all this without his nunchucks.
Raph and his new friend Tyler get one in Lone Raph and Cub. Raph is capable of handling the mobsters without breaking a single sweat, until one of them blinds him. With some help from Tyler, he manages to take down the mob boss.
Splinter, April, and Casey infiltrating Bishop's lab to rescue the turtles all while two evil alien races are fighting each other. Noteworthy in that Splinter had to teach April and Casey the same ninjitsu techniques that took the turtles 15 years to learn within minutes.
Splinter: The way of invisibility takes a lifetime to master, circumstances however, require us to learn as we go.
How has "Prodigal Son" not been mentioned? For a chunk of season 4, Leo has been letting his rage at his perceived failure to protect his family during their last fight with Shredder eat at him. So, Splinter makes him go see the Ancient One, the master who trained Hamato Yoshi, and he gets his issues sorted out. In his absence, Karai becomes the new Shredder and attacks the remaining Turtles and Splinter. In the actual episode mentioned, Leo returns, locates and rescues his separated family, then delivers a Curb-Stomp Battle to Karai, who he's never managed to beat before. And capitalizes it with a promise to finish her if she ever goes after his family again.
"Wedding Bells and Bytes" was an excellent way to end the series. Not only did the show makers manage to get almost everyone who had interacted with the Turtles to show up at the wedding (And those that couldn't make it or weren't invited somehow manage to watch), but the battle against the Foot Clan was great too, with everyone fighting.