Sinful Behaviors has Mr. Cosmo. Throughout most of the story, he is calm and collected, rarely raising his voice. By the end, when everything is falling apart, he snaps and attacks Rudy blindly in a desperate attempt to kill him. This results in his untimely death.
Play The Game, the sequel, has a more terrifying example with Bardot. Like Mr. Cosmo, he manages to keep his cool, but his tempers flare up a bit more frequently. And when Snap manages to exceed his expectations in a way he did not enjoy, Bardot becomes feral and proceeds to tear apart an already mortally wounded Snap.
Gilda grows gradually more ballistic as Rainbow Dash gains advantage over her during the final duel.
Mecha Sally in Apprentice is really emotionless when it comes to taking Eggman's orders. That is until Sasuke Uchiha comes by and started beating her up, showing he's better than her. With that much insults coming out of him, Sally sure is started to have a breakdown.
Burning Black has Remy Buxaplenty suffering from the gradually progressing type. It's very alarming to his fairy, Juandissimo, and just as alarming to Timmy. It seems to get worse with every new fact he learns about Timothy and every Dark Spire that gets destroyed.
The version of Lisa in The Flynns Move To Springfield gets a big one at the end, cementing her story-long Sanity Slippage. Lisa's attempts to sabotage Isabella's moment in the limelight actually helps her. At the end, frazzled, humiliated and stark raving mad, she walks up to Isabella backstage and, not realizing everything that she says is being recorded, accidentally outs herself as the cause of all the accidents that occurred.
She gets an earlier one where she is screaming revenge on Isabella (who is the centre character here, despite the title), while strangling and hitting Maggie. Before then she was an Affably EvilVillain with Good Publicity, after that scene, she becomes more pshycopathic as she gradually loses her sanity.
In the Zero no TsukaimaFate/stay night crossover The Hill Of Swords the villainess Sheffield starts out as a Smug Super supremely confident mage that swiftly devolves into a raving lunatic as Shirou outmatches her in each of their encounters. During their final encounter in chapter 22 she spends quite a bit of it just shrieking "DIE!" as Shirou refuses to do just that. The breakdown is so bad that she falls for one of the oldest tricks in the book: the old "your shoelace is untied" gag.
The Stars Will Aid Their Escape: Herald actually gets angry when the Princesses, in their true forms, begin to win against him, damaging him faster than he can heal, symbolized by his mask being cracked when he returns to the mortal plain. While he maintains his composure, he loses enough of his Genre Savvy to leave himself wide open to the Elements of Harmony.
Herald: “Your Majesties... you are beginning to frustrate me...”
The S’Müz pretty much freaks when the ponies start stealing its PKE, killing it.
In the sequel Mines of Dragon Mountain, Tirac ends up frantically begging Gabbro not to stop him by jumping into a lava pit and dragging him in. And then Gabbro does it anyway.
Happens to Ludlow in Rise of the Galeforcesafter Violet forces him through an epic Humiliation Conga. After all of his contingency plans fail, he shoots her in the back, and when she is revived, he sings "Rock of Ages" and starts hallucinating about going to heaven. Too disgusted with the guy to want anything to do with him at this point, Violet sics the baby tyrannosaurs on him, and the last thing he hears is his own terrified screaming as he is ripped to shreds and devoured alive.
When Actrise realizes that Twilight's Out-Gambitted her by channeling a spell through Dracula's rib to the other body parts to hide them, she starts screaming Twilight's name while beating the Chronomage (who was unfortunate enough to be standing next to her) bloody with her staff. She calms down after a few minutes, but is now determined to see Twilight dead at her hands.
Steel Wing loses it after Luna arrests him for harassing Supermare, constantly ranting about the Princesses being in a conspiracy with Supermare to take over Equestria.
Brainiac's is much less noticeable, but after Supermare manages to defeat his supposedly foolproof Sadistic Choice, he actually gets angry and decides that instead of adding her to his collection, he'll just kill her.
"Kara Jor-El... You have become an annoyance."
The Princess of Themyscira: Ares completely loses it during the Final Battle when Diana manages to destroy the Alicorn Amulet and close the portal he's opened to Tartarus. He's left desperately trying to keep the portal open and when he starts getting sucked in, lashes out and grabs Diana in an attempt to drag her down with him.
In And Again, the Mastermind behind the Deadly Game of Danganronpa throws a hissy fit when their mole murders one of the others, then promptly confesses to the crime, denying them the pleasure of a drawn out, dramatic trial and execution. By the end of that loop, they completely break down when Naegi reveals her staged murder as a hoax, meaning her game ended with only one murder, no real trials, and none of the drama and despair she'd been hoping for.
Queen Of All Oni: Lung starts cracking when it becomes evident that his plan to break Jade to his will is failing, and then he breaks completely when her minions show up to save her.
Drago eventually has one due to the repeated failures of his attempts to gain power in the past. He ultimately snaps and rants that rather than doing things strategically, he's just going to smash everyone and everything in sight and see what effect that has on the timeline. Fortunately, he's banished back to the future before he has a chance to.
Jade herself has one when her PTSD from Lung's actions finally hits a breaking point. After Tohru's failed attempt to capture her in the Vault of Endless Night, she snaps, becoming paranoid and delusional, convinced that the heroes (and humans in general) are out to either seal or kill her (and her emotional confrontation with her father doesn't help, least of all the reveal that she was accidentally conceived and nearly aborted).
In the All Things Probable story, A Friend In Darkness, Monkey Fist, who was usually the most calm-minded and suave villain in the cartoon, suffers from one of these in the final battle of the story after being humiliated, reducing him to raging and shrieking like an actual monkey while unleashing the dark power he had been cursed by. The irony is, his breakdown wasn't caused by Ron Stoppable, his actual Arch-Enemy and the one more likely to drive him into one.
In Girls' School, Lucy Horowitz, a girl accused of holding down another girl as the other girl was raped, has one after learning that the rapist was caught, thus denying her a bargaining chip for a reduced sentence.
In A Dark Beginning, Dredd, the commanding Ape on the Tall Plains, has one of these after he discovers Kane escaped, going from Faux Affably Evil to screaming his death threats and his You Have Failed Me trait surfacing. After he falls for Spyro and company's plan to free and arm his captives, resulting in his entire group to be wiped out, he's left stunned at what happened before getting enraged and going into a Last Villain Stand against Kane that leads to his demise.
In Project Gethinator, the Big Bad, Admiral Daro'Xen, who is Yandere in a big way for Commander Shepard, loses it quite spectacularly after Shepard decisively turns down her advances and calls her on her crazy scheme and her obsession with him. Her breakdown is of literally star-system-shattering proportions — she takes the same mineral scanner that Prazza, Tali's idiot crewman from Inglorious Boshtets, accidentally used to make a star go supernova and uses it on the main star of the Eta Carinae system to make the thing go hyper-nova, making sure to have the Normandy's drive core disabled so Shepard, Tali and the crew cannot escape. When the crew does manage to escape Just in Time (via Shepard's quick thinking and Legion's advanced skills getting everyone out of there alive), Xen proceeds to lose it even further.
A Brief History of Equestria has Sullamander (the pegasi Supreme Commander before Hurricane), who wasn't quite sane to begin with, completely fall into anger, paranoia, and madness during her last days as Hurricane and his lover General Wind Whistler led a successful coup against her. Her last confirmed action (everything else being unconfirmed myth and rumor) before her final duel with Hurricane was to accuse her loyal generals of being traitors and killing them, before fighting Hurricane to the death; during the fight, it seems she didn't even notice her large assortment of wounds, being so solely focused on killing her rival.
Viscount Arsenic ended up falling apart during the Lake Trot Crisis, due to his supposedly superior troops being curbstomped by the Hyracotherium Republic forces under Lady Cripps (the fact that she was a mare contributed to it). This eventually led to him trying to personally lead his forces in the final naval battle of the conflict, which got him killed.
Earth and Sky: Diamond Tiara breaks down completely in light of all her plans falling apart, being captured by the changelings, and then being left to die in the badlands by them because even they can't stand her. By the end, she's so broken that the only thing keeping her going is her hatred for Apple Bloom and her determination not to see her rival beat her. She starts to get better when her life is saved.
Professor Destiny completely loses what sanity he had left after he and his brother are disqualified from the race. He becomes determined to finish the race no matter what, and basically turns their flight harness into a weapon and the race into a suicide run, not even caring when they're about to hit the shield covering Canterlot. They survive, and it seems he finally had some sense knocked into him.
Then, what little sanity she has left goes out the window when Helping Hoof and the Diamond Dogs turn on her and help Trixie and the Mane Six set up an Engineered Public Confession.
The Immortal Game has a couple. First, Nihilus — who wasn't all that sane to begin with — completely loses her shit when Rainbow Dash not only breaks free of her mind control, but she learns that she hasn't corrupted the Elements of Harmony, as she thought. Then, near the end of the story, Empyrean totally falls apart when the Mane Six break into his throne room to confront him, and fires off the magical equivalent of a Wave Motion Gun to try and fry them only for the Elements to be used to strip his powers instead.
Inner Demons: Twilight Sparkle stopped being sane the moment she was consumed by her Queen persona, but even by that standard she really flips her shit during the Battle of Fillydelphia when she realizes that her beloved brother is choosing to stand against her with the protagonists. She starts ranting and screaming that she'll kill all the heroes, Shining Armor included, and is only stopped from carrying out an execution on Cadence by the other heroes arriving in time. Interestingly, they also somewhat accidentally calm her down from the breakdown when they then confront her over Trixie (nearly) killing Rarity on her orders.
She has a much more severe breakdown when Trixie — the only pony left she felt she could trust and call a friend — dies right in front of her. She starts laughing and crying, before the emotional trauma causes her to transform into an Alicorn. She then declares that she's going to unleash the hordes of Tartarus, because if she can't be Equestria's ruler, she'll be its destroyer.
On the plus side, the shock of all this disrupts all her spells, thus restoring Cadence's powers, freeing Luna and the Royal Guard from her Mind Control, and freeing Celestia from her stone imprisonment.
My Little Mages The Nightmares Return: Nightmare Moon, after spending the whole story in a self-assured confidence that the heroes can't even hurt her let alone stop her, panics when they manage to active the Elements of Harmony, and flies into a blind rage when they actually manage to hurt her. As is pointed out in the story, she even stops using the Royal "We" she'd been using all story.
The Nuptialverse: At the climax of Families, Olive Branch completely falls apart when Celestia laughs in his face, pointing out how incredibly flawed his master plan is, and he realizes she's right. By the end, the formerly smug manipulator is wildly crying and begging the Princesses not to hurt him as he's dragged off and arrested.
Loneliness from the Pony POV Series loses her cool a bit every time Twilight manages to fend off her mind games, but snaps completely once Twilight actually manages to break through to Trixie. Loneliness goes One-Winged Angel and drops her facade of "love" towards Trixie, breaking her leg and outright trying to murder Twilight rather than let Trixie escape her clutches.
Discord has two in "Origins". The first is when Mimic reveals to him that the bridge between Ponyland and Earth has been destroyed, thus protecting humanity from him. Discord is rendered speechless for a few minutes and left so beside himself with anger as to forget he's an omnipotent Reality Warper long enough for Mimic to perform her now famous Dying Moment of Awesome. The second comes when Shady, The Dragon and earthly mother whose love for him he's manipulated for 1000 years, betrays him, allowing Celestia and Luna to defeat him.
During Mind Games, while he's working on breaking Diamond Tiara, she somehow views his memories of being raised happily by his mortal mother Shady (Diamond's ancestor). This causes Discord to flip out.
A flashback during the Dark World arc reveals that the Epilogue version of Discord had another one when, in the aftermath of an attempted Alien Invasion of Equestria, he went after the aliens' leader, only for him to take pity on the sick old man and return him to perfect health for a day. The breakdown occurs as a result of Discord having no idea why he did it, even after Twilight Tragedy explains it to him.
Also in the Dark World, Traitor Dash slowly loses it over the course of the Duel of Tears, as she desperately tries to kill Twilight, all while trying to convince her, the others, and herself that it's the right thing to do. Twilight actually invokes this to defeat her, and then uses the memory spell to restore her.
General-Admiral Makarov, the Big Bad of the Shining Armor Arc, has a small one when Sergeant Thunderchild ruins his plan to capture and/or kill Shining Armor, though he recovers quick enough to order a retreat of his forces.
The Valeyard ends up having one as well when the Dark World Elements of Harmony discover that he's using a regeneration template to preserve his personality and he starts frantically trying to stop them from exploiting this fact to beat him. He fails.
Again in the Dark World, Fluttercruel has one when Rarity turns the tables on her by shooting Tom'sfragmentthrough her eye and subsequently manages to mortally wound her. Fluttercruel basically throws a temper tantrum, screaming how Rarity "cheated" and calling her every profanity she can muster until Rarity finishes her off.
After surviving by possessing Sparkler's body, 'Cruel starts to crack as the heroes start to poke holes in her life philosophy (expressing love through violence and torture), but doesn't have a full emotional breakdown until Rancor betrays and mortally wounds Discord. She's unable to accept this and blames it on the heroes, before she absorbs the Shadows of Existence and turns into a full Draconequus, and starts ranting on how she'll kill them and everything else until she and her father are all that's left. By the time the heroes defeat her, she's reduced to a ranting, screaming, whimpering mess who was hallucinating for most of the fight.
During the same fight, Rancor has a relatively mild one when Spike turns the fight around and she actually starts feeling pain. She goes from smug Affably Evil villainous to whining like any teen not getting their way. Justified because she is a teenager (relatively speaking) and being immune to violence means she hasn't gotten hurt all that much, and thus hasn't experienced pain frequently enough to build up a tolerance to it.
The Nameless Passenger/Nightmare Eclipse/Paradox has several over the course of Dark World, but always manages to recover. However, as the Final Battle rages on and the heroes keep countering her attempts and the Big Damn Heroes keep showing up, her composure begins to slip more and more frequently as her frustration and anger mounts. The Benevolent Interloper even mentions she's getting more and more desperate. This reaches its zenith when Minty Pie enters the battle and refuses to stay down, ultimately thwarting her attempt to corrupt Twilight.
Throughout "AJ's Dreams", Nightmare Mirror stays calm and speaks in an even, cultured tone. But as Applejack and Orangejack continue to defy her, the more she starts to crack, along with her voice starting to degrade back into her normal country accent.
The Defense Attorney in the trial for Starlight's soul in her 7 Dreams/Nightmare story has one when Starlight declares herself guilty and is forgiven by the Prosecutor. She goes on a tirade, flipping the table over and screaming Starlight wasn't supposed to be forgiven...then laughs and says it was fun. Turns out "she" was Havoc the entire time (the Father of All Alicorns was the Prosecutor) and He pretended to have a breakdown when he saw he was losing because It Amused Him.
The Master has one when Minuette resists his attempts to tempt her into opening her fob watch and become him again, eventually losing his cool and screaming at her.
The Master: YOU EQUINE FOOL! You are ME! You are the MASTER!
Queen Chrysalis has one when Blueblood arrives with the real Cadence at the wedding, becoming so enraged she tries to vaporize him, blowing her cover and forcing her to reveal herself. She manages to regain her composure and the advantage, but she spends most of the chapter openly furious.
Kerrun as she realizes that the four aren't on her side after all; and, later, when she goes off the deep end completely and declares that every skahs in Ehndris is actually an Idri.
Jeft has two:
When the Hunter makes friends with the four instead of fighting them, Jeft is so pissed at this subversion of his favorite gaming character that he sics square miles of undead on them as payback. He freaks out completely when the five manage to destroy the Heart of Evil powering the whole show.
A few hours later, when the Hunter agrees to ditch his BFS in order to return to C'hou with the four, the still-simmering Jeft goes crazy with anger and turns the sword back into the demon it always was in an attempt to kill the four and regain control of the Hunter.
In Ultimate Spider-Woman: Change With The Light, Spider-Woman's Arch-Enemy Jack O' Lantern's sanity has been going downhill for a very long time. Developing an increasingly crazed obsession with his teenage nemesis for her constantly interfering in his "fun", he hatches a plan to mentally break her and make her his heir. When she overcomes that, he goes berserk in an attempt to kill her. When she defeats him and he's hauled off to jail, he's raving insanely in his cell and hallucinating everything from screaming witches, dancing skeletons and flaming pumpkins to giant human-headed spiders that alternately have the face of Spider-Woman or her civilian identity of Mary Jane Watson.
There's a fanfic where the author takes the plot of WALL•E and humanizes all of the characters. And Human!AUTO's breakdown is... well, it's a much worse version of the one in the original film, since he's an indoctrinated officer, bent on following orders completely. He isn't sane already, and seeing the orders he was raised to follow being broken isn't very good for temper and mental health. Humanizing him made his breakdown much scarier.