All of Case 5. Continue reading for more specific examples.
Gumshoe's Big Damn Heroes moment in I-5, when he runs in yelling how he's sorry he's so late, bringing with him the evidence you so desperately needed. How did he know to look for said evidence? His detective instincts nagged him into doing it. You didn't even have to ask, but thanks to him you could prove how the killer moved the body.
Ace Attorney Investigations has a couple of these; for example, Shih-na grabs Kay and uses her as a body shield and holds a gun to her head... only for the sound of ANOTHER revolver being loaded to be heard and the camera panning back and showing Badd with a gun to Shih-na's back.
Then Lang takes the bullet for Shih-Na, and seems to just shrug it off because he's simply that badass. He then justifies his action, saying that he has a duty to his subordinates, even if they're sociopaths who only joined his organisation so they could act as a mole. All the while grabbing Shih-Na and forcing her into a somewhat compromising position.
At the beginning of the game, an unknown perpetrator holds Edgeworth at gun point and even gives him a warning shot. Edgeworth doesn't even flinch! It's a double awesome given that Edgeworth has some extreme issues with guns, what with spending fifteen years thinking he murdered his father and hearing the sound of the shot in his nightmares.
Edgeworth: No one gets away with committing murder in my office. No one.
From the same case, this line from Edgeworth.
Edgeworth: I believe the proper phrase here is, "you fail."
The game itself is a Crowning Moment of Awesome, the fact that we control Edgeworth, and how he took down the head of an international smuggling ring that interpol agents and the Yatagarasu was pursuing for seven years, in less than 48 hours after learning the existence of said ring. Miles Edgeworth > Jack Bauer.
In Case 5 of Investigations, Lang gets one for creating a Batman Gambit by forcing Franziska herself to be a murder suspect just so they can access THE OFFICE OF AN AMBASSADOR!
The most epic and satisfying sentance ever uttered in video game history: "Your Diplomatic immunity...has just been revoked!"
In the same case, Lang catches Franziska's whip mid-lash!
Speaking of Franzy whipping, Badd dodges her in case 4! He then proceeds to make a joke about having her arrested, which makes her back down. As Edgeworth puts it...
Edgeworth:Detective Badd is really something if he can make Franziska behave...!
In case 5 of AAI, the big villain is prevented from escaping by previously harmless Nice Guy Ambassador Palaeno, who persuades him to stay for a while so as not to damage the relationship between their countries. Palaeno subsequently announces that it doesn't matter that the victim was a total crook, he was Palaeno's subordinate, and thus Palaeno must fulfill his duty to him.
In the same vein, Larry Butz and Wendy Oldbag, as ridiculous as it may sound. The two pull off a rather dramatic entrance in their Steel Samurai and Pink Princess costumes to prevent Quercus Alba from leaving and both end up giving Edgeworth some crucial information that puts Alba in his place without even knowing it! Oldbag deserves special mention as her clue (a single Samurai Dog box with a spot of blood in it) was so crucial that Edgeworth actually thanks and even bows for her!
Lets not forget that Larry Butz played the role as the STEEL SAMURAI in a show that was part of a good-will celebration between two countries, and acted as a good-will ambassador for both countries and the one the embassy is based in as well! That's impressive going.
The end of Case 5 of Investigations:
Edgeworth: Mr. Alba, I'm afraid there is one more question I forgot to ask....
Edgeworth: This country's, or Allebahst's: Which country's court would you like to face first? Either way, it's game over for you.
In Case 5 of AAI, what about the little forensics guy who shouts HOLD IT! so he could inform everyone that he wasn't finished talking? Awesome stuff, considering who he was speaking to at the time.
In the sequel's Case 3, just about every time Gregory confronts von Karma. But the final time really stands out, after using Logic to find out von Karma has been manipulating the crime scene and forging evidence, he walks up to him and yells HOLD IT while giving him the pointer finger. When von Karma accuses him of disrupting the police investigation, Gregory delivers this line:
Gregory: "Police" ...no. My objection is to you!
The resulting confrontation is nothing short of epic, and for the first time in the case Manfred completely loses his composure. It's clear no-one has ever managed to utterly humiliate von Karma like this, and Gregory makes it even more awesome by being in full Tranquil Fury mode practically the entire time. And while you don't actually get to play the trial itself, from Tateyuki's description it was clearly one huge CMOA for Gregory and cemented his status as a complete and total Badass. Not only did he prove von Karma forget evidence, he was able to present tapes of his interrogations to show the entire court he bullied the defendant into giving a false confession. He managed to get von Karma's (corrupt) replacement detective fired, and Manfred himself only got off with just a penalty because the Chief Prosecutor at the time was just as much of an Amoral Attorney as he was, and actually had a hand in the forgery, so he had to give Manfred some punishment or he'd give himself away.
Yumihiko: I'm...I'm fine now. I thought that I had to be Number One so that you would accept me, dad. But then, after I got kidnapped by your men and left in that dark storeroom, I realised..."I really am powerless". I became depressed, and tried not to see that...but then...but then, Prosecutor Edgeworth showed me the way. I'm no longer a child chasing after his dad's back. I CAN find evidence on my own now!
Making it even more awesome is that, at this moment, Yumihiko replaces his old, goofy Leitmotif for THIS.
A villainous one occurs for the set up of Case 5, Souta manages to encounter fake President Ou by luck whilst in his hot air balloon. Seizing his chance proceeds to crush him under the basket, in spite of the fake being armed with a handgun. He then hides the body and manipulates it so he evades capture for quite some time.
There's also the fact that he was pretty-much behind everything in the entire game. And unlike the Big Bad of the previous game, he's not the head of an international criminal organization or anything, he's pretty much just a clown at the local circus. Not only that, but the fact that he actually appeared before, and yet likely never aroused any suspcion in Edgeworth or the player, is one for both his character and the game itself.