Evidently, life-threatening situations bring out our hidden powers. Do not try this at home, though. The threat seems to have to come from Fate for it to work out.
At a moment of extreme stress, a superpower pops out that the character never knew was there. They might have continued to lead a normal existence, doomed to be — at best — a character in a romance, if it had not been for that car wreck, or fall from a great height, or evil-doer...
A preferred training method of the Sink or Swim Mentor. Contrast with New Powers as the Plot Demands, which is about powers manifesting as an easy way out of danger. This trope is about danger being used as a not-so-easy way for powers to manifest. This trope is a common way of introducing Powers in the First Episode. If the power can only ever be used in life-threatening situations, it's a Defence Mechanism Superpower. Compare with Traumatic Superpower Awakening, when the powers appear as a result of trauma that is not immediately life-threatening.
This trope is the central concept of Japanese Spirit.
A Death Activated Superpower is when both happens. They die, then they fly.
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Anime and Manga
In Naruto, Jiraiya resorts to literally throwing Naruto off of a cliff to force him to learn how to tap into the power of the Kyuubi demonsealed within him. Luckily for Naruto, this "strategy" actually works and enables him to get the chakra needed to summon a giant toad.
Also, the Uchiha clan's hereditary super-eye power, Sharingan, first manifests in a life-or-death situation. For some reason, they can use it at will afterwards, although it takes time to get to full potential.
Naruto's first successful use of the Rasengan is in his battle with Kabuto, in a situation in which failure would have meant defeat.
Mai's powers manifest themselves this way in Mai-HiME, after Natsuki attacks Mikoto and she tries to defend her.
In Bleach, Ichigo goes through this several times, the most noticeable being the point where he has to learn to become a shinigami before he turns into a Hollow that needs to be put down. But the biggest and first example is when he first got his powers; the only way to do this was to cut his chain of fate which should be a death sentence for a living soul. He was told the only way left for his life to be saved was to find his hidden shinigami powers... or die.
Orihime and Chad's powers also manifest the first time when they are threatened by Hollows, Although Orihime managed to call out her power not so much in defense of her own life, but at the desperation to protect Tatsuki and her other classmates.
The 2003 anime version of Astro Boy, which addresses the ridiculousness of his various built-in gadgets by giving him a highly modular construction that reconfigures itself in response to danger. He gains his iconic rocket boots after tripping and falling out the window of a high rise office tower.
Also used in the 2009 movie; the rocket boots activate under similar circumstances, while his weaponry activates in moments of crisis during the final battle.
In the Hiryuu Shouten Ha story arc (Rising Dragon Wave in the US) of Ranma 1/2Cologne never gets around to disclosing the legendary technique's final step to Ranma. However, he figures it out all on his own just as Ryouga's fist is about to turn him into paste on the side of the mountain.
The Nekoken of Ranma ½. Cover a child in fish. Throw them into a pit full of starving cats. The child learns or dies.
Retasu in Tokyo Mew Mew gained her mermaid form when she jumped into the ocean, despite being terrified and unable to swim, to try and save a small child. Technically, a Mew Aqua also helped.
Hayato Kazami and Asurada learn the Lifting Turn in Saga completely by accident. Asurada in its AKF-0 version bounce off course during a test drive and in order to avoid a painful crash landing and keep Hayato, its driver, safe, it reverses its effect fans and causes the car to float around the turn. Lo and behold, Hayato's just discovered his most gamebreaking driving skill ever.
Before that, he learns the Internal Drift when Super Asurada AKF-11 is about to crash on the wall, also during a test drive.
Basically the whole point of +Anima, where people's ability to "transform" first manifests when they are in extremely dangerous circumstances.
In Grappler Baki, a young Baki throws himself off of a cliff in order to trigger "endorphins" that enhances his senses.
In One Piece Zoro comes up against an adversary whose body is made of steel. With no option to retreat, it becomes a "cut steel or die" scenario. No points for guessing the outcome. It's even lampshaded to an extent, when Zoro declares, after learning of his opponent's ability, that he will be able to cut steel by the end of the fight.
Garp's preferred training method, especially when it came to his grandchildren. Then when he realized that his being away from home for so long did not work towards his goal of making them marines, he left them with a friend to raise them and make them marines. Said friend was a mountain bandit. He was asking for it, really.
Early on in Dragon Ball Z, Piccolo throws Gohan at a mountain for this express purpose. Good thing it worked. Of course, instead of flying, Gohan goes into "hidden power" mode and vaporizes the mountain, which was a lot more than Piccolo expected.
The above was foreshadowed in Gohan's first appearance, where he was about to go over a waterfall. When Goku arrives, he's somehow clinging to a branch far above the fall with no idea how he got there.
At the end of the Soul Eater anime, Maka discovers that she is also a weapon, like her father when fighting Kishin, though this is not what allows her to defeat him.
Gundam X has Newtype powers work this way, as demonstrated in the Estard arc. The Frost brothers sic potential Newtypes on the Double X, with the intent that the near-death rush of battle will awaken their powers. Out of the four Pilots of the Week, only the last one develops powers in this way. Which is just fine by the Frosts, who despise Newtypes and were sending the candidates to their deaths; the one who does develop powers and survives his fight gets shot anyway.
In the first chapter of Busou Renkin, Kazuki learns how to summon his Busou Renkin in the course of defending himself from a giant robotic cobra.
The first time Leina pulls off the Dragon's Tail in Queen's Blade is during her training session with Echidna. Said training session? Echidna openly and actively trying to kill her for three days straight. (Both combatants are coated in sap that prevents any injuries, but that sap does wear off over time...)
This is how Eren's titan shifting ability was awakened in Attack on Titan when he was in the belly of the titan who ate him. Also, his ability as the coordinator manifested when their group was surrounded by titans outside the wall with little hope of surviving.
In the Marvel Universe there is a relatively new phenomenon called Secondary Mutation, in which known mutants (typically X-Men) suddenly develop a new mutant power at extremely convenient moments, such as a healing power (after receiving an otherwise mortal wound) or the ability to become indestructible (in the middle of a bombing). It started as an excuse by Grant Morrison to give Emma Frost transform-into-diamond powers, since he had was not allowed to bring the transform-into-metal Colossus back from the dead, and had a story idea he wanted to use.
The Richard Rider Nova is not a mutant, but he was depowered for a long time and the superhero, Night Thrasher, guessed that he could reignite Rider's powers with a high stress incident. To create one, he kidnapped Rider, dropped him off a building and found that his hunch was right when Rider instantly repowered in the fall, including his flight power.
He tried it a second time after another depowering, only to be rescued before the splat and having it made very clear that a second power up was not what would have happened (he got his powers back again of course in another storyarc).
Spider-Man first discovered his powers this way. While walking home feeling sick after being bitten by the spider, a car is about to hit him. His new Spider Sense kicks in and he instinctively leaps up the side of a building and clings to it.
The transformation of Jean Grey into The Phoenix was originally presented as this, then retconned into a subversion, with a primal power of the universe using her as a template to create an avatar. (This ultimately went horribly wrong.)
Wolverine is a prime example of this-his claws first popped out during the attack on his parents.
In its 1988 Crisis CrossoverInvasion!, DC Comics introduced the "metagene", which gives humans superpowers as a way to survive lethal trauma, as a way to Handwave the many heroes and villains with Freak Lab Accidentorigin stories. The concept was demonstrated by an alien scientist performing a mass execution of fifty abductees; six of them survived, gained powers, and briefly formed a superteam.
Superboy later introduced a character called Sparx, who came from a family who had all tested positive for the metagene. Members of her family deliberately endangered themselves to try and trigger their powers.
Another story featured wannabes hanging around hoping for the day of their Origin and one relating how one guy decided to stop waiting and shoved a fork into a toaster. While the guy he's talking with starts rattling off possible powers the answer for what it got was 'electrocuted'. Destiny doesn't like it when you try and cheat.
There is a Sandman short in which a dreaming man who falls off a cliff literally must fly or die. It ties into An Aesop about how you don't know if you can do something until you've done it.
In Strikeforce: Morituri, candidates for the Morituri Process must survive Biowar Facility Alpha, a greenhouse garden loaded with lethal traps. The stress of survival is required to trigger the superpowers granted by the Process.
In ElfQuest, Zahntee's shielding power first manifests when he saves Skot and Krim from being struck by a falling branch. Justified in that this is the first opportunity he'd had to invoke it after being exposed to the Palace, which enhances elves' powers.
The original Liberty Belle, a member of the All-Star Squadron, had an experience like this. She'd been kidnapped by Baron Blitzkrieg, who used her, a lightning bolt, and the stolen Liberty Bell in an attempt to cure his blindness (don't ask). The experiment worked, but the bell fell off its rig toward Libby; she raised her hand in a desperate bid to stop it, and it flew across the room, hitting Blitzkrieg instead. Turned out the experiment had given her sonic powers as a side effect.
In Wanted this happens where Wesley must shoot the wings off of flies or Fox will blow his brains out.
The "Pureheart the Powerful" sequences of Archie (1966-7) had this as Betty/Superteen's origin story, as she tried to rescue an unconscious Archie from falling off a cliff.
This is Darwin from X-factor's main power. He always mutates the most simple and convinient power he needs to survive whatever situation he's in. This can range from surviving without a head, to being part Death, to teleporting out of the way of an angry hulk.
A Running Gag in the French comic Raghnarok: the titular Raghnarok is a young dragon who has yet to manage to fly, so his mother tosses him off a cliff every chance she gets (Amusing Injuries are in full effect, so he only get bumps, bruises, and an ever-deeper aversion to flying from the whole thing).
John in With Strings Attached, when he is held prisoner in a net he can't break and furiously wishes he could turn into water. Splash! Though the experience almost drives him crazy.
Also Ringo, twice. First, he has his choice of telekinetically levitating himself (which he's never thought to do before, because he can only hold something 5-7 seconds) or getting torn apart by crazed "Beaglemaniacs." Then, after a pair of disembodied arms throws him off the garage roof where he stranded himself (It Makes Sense in Context), he suddenly teleports to safety—if ending up in the Plaza Hotel, currently under siege by thousands of Beaglemaniacs, is "safety."
In the Negima fanfic 'Fang Vice Addiction', this is how Evangeline tries to teach Negi to fly without a broom. It repeatedly fails, with her having to rescue him, so eventually she just jumps herself, expecting him to save her. It works.
In the MLP:FiM fanfic Aurora, the Big Bad (and Twilight Sparkle!) ascend to a higher plane of existence in moments of desperation. The Princesses' moments of desperation are worthy of terror...
The Powers Of Harmony invokes this when Blair, on Ophiuchus' insistence, forces Twilight to get over the mental block on using her powers by tossing her over Neighagra Falls. To say that she's not happy afterwards is an understatement.
In a rare case of Die and Fly, it is a violent death that causes potential immortals to become actual immortals in Highlander: unless immortality is activated in this way, they remain vulnerable to peaceful, timely death. This becomes a major plot point in Highlander: Endgame.
The movie Puma Man (featured on Mystery Science Theater 3000) had Valdhino toss random people out of windows in order to find the man who has the Puma Man powers. He finally hits paydirt when he tosses Tony out and he lands on his feet like a cat.
In The Incredibles, Jack Jack apparently doesn't manifest his powers until Syndrome tries to kidnap him. However, the short film "Jack Jack Attack" reveals that Jack Jack did manifest his powers beforehand: a Mozart CD is the catalyst. The sitter did say that Mozart is good for babies, I guess she just didn't know the effects on superbabies.
Happens to the hero twice in Sky High. Once literally.
In Jumper, the main character Jumps to avoid drowning after he falls through thin ice into a frozen lake.
Not quite the discovery of superpowers, but in the same vein: at the end of the Animatrix short Kid's Story, the eponymous Kid frees himself from the Matrix by throwing himself off the roof of his school.
In Unbreakable, David discovers his invulnerability after surviving a horrific train wreck unharmed. Turns out his mentor, Elijah, was behind it because of this trope; he has caused many disasters in order to find someone like David.
The climax on the film Rio. Blu must fly or he and Jewel will die. And he did.
There are several examples in X-Men: First Class. First, in a case of Die Then Fly, Dr. Schmidt threatens to shoot Erik Lensherr's mother unless he figures out how to use his power to move a coin. Erik is unable to do so until after Schmidt kills his mother, the pain of which triggers his abilities. Later, Erik takes a literal Die or Fly approach during Sean Cassidy's flying attempts, while Alex Summers grasps his energy-blasting ability just as he needs to.
The film version of Fantastic Four also has this. Johnny has been trying to master flight ever since he got his powers (with no one really believing he can do it), when Doom fires a heat-seeking missile at the Baxter Building he leaps off the edge to try and lure it away and right before he splatters all over the pavement he finally nails it.
Gully Foyle of Alfred Bester's classic SF novel The Stars My Destination suddenly can "jaunt" (teleport) much further than anyone has managed before when he is marooned in space — and then gets really ticked off.
"Jaunting" started as "burn or teleport" for the discoverer, Charles Fort Jaunte, about a century before. He was later put in an inescapable, slowly flooding chamber by his fellow scientists to force him to replicate the process.
In a more literal example, the Harry Potter books mention that Neville Longbottom's Uncle Algie made multiple efforts to "scare" Neville's hidden magic into manifesting when he was a baby — most notably by throwing him off a pier and dangling him out a window. Neville's magical nature was finally revealed when Algie simply dropped him by "accident" — and he bounced.
ON a less literal example, Harry finally masters a difficult spell when facing the prospect of playing chase with a dragon.
Bran's first dream sequence in A Song of Ice and Fire. To all appearances, this does save his life, but the poor kid would be a lot happier about the flight he was promised if he could grasp a metaphor.
In the Matrin novels by Holly Lisle, the shape-shifting characters only fly after dropping out of a building, or off of a mountain.
In Steven Gould's novel Jumper, Davy first "jumps" (teleports) involuntarily to escape his abusive father. At first he thinks he just blacked out after his dad beat him, and began hitchhiking. The first time he consciously realizes he "jumped" is when some truckers tried to rape him, and he was suddenly back in the library.
Happens again in the sequel, Reflex, in which the main character's girlfriend-in-the-first-book-wife-in-the-sequel "jumps" to safety after a probably-fatal fall. Apparently, being teleported by a teleport enough times can pass on the ability, though the characters have NO idea how that works.
In Audrey Niffenegger's novel The Time Traveller's Wife, great stress seems to be the activator of involuntary Time Travel. The time traveller mentioned in the title uses his power for only the second time, completely involuntarily, to escape from the car crash which killed his mother. And then later on, he gets to travelbackto this moment and watch it from the sidelines at multiple angles...
In the Wild Cards series, people infected with a latent version of the wild card virus often "turn their cards" after a near-death experience. Examples include Will-O'-Wisp (stepped on a power line, gained electrical powers), Stuntman (botched a stunt during a student film and fell several hundreds of feet onto solid ground, gained the ability to regenerate from any injury), and the Harlem Hammer (exposed to nuclear waste, gained superstrength and invulnerability but needs to consume heavy metal salts to survive).
This is exactly how Arthur Dent manages to fly, after reading from the guide that flying is the art of "throwing oneself at the ground and missing" - he has to completely focus his attention on something else (typically something immensely banal, as per the themes of The Hitchhiker's Guide to the Galaxy) or simply forget that he's supposed to be falling. Once achieved, he simply hovers there and can move around at will... but he has to be careful not to think too hard about what's going on.
The Hitchhiker's Guide to the Galaxy (on flying):...Do not listen to what anybody says to you at this point because they are unlikely to say anything helpful. They are most likely to say something along the lines of, 'Good God, you can't possibly be flying!' It is vitally important not to believe them or they will suddenly be right.
Perrin (walking off a cliff): It must be done. I must learn to fly before I reach the bottom.
This probably refers to his mastery of the World of Dreams, particularly his Eleventh Hour Superpower of moving between the dreaming and waking worlds at will. He had a mentor, albeit a tough one, for most of it, but that particular trick was one that only one other person had ever accomplished, and that through very unusual means.
This is also how Nynaeve finally overcomes the mental block that prevents her accessing the True Source unless angry. Trapped in a sinking ship, her only option is to fully surrender to the Source, and thereby control it.
In the world of Belgariad and The Malloreon, David Eddings uses this trope straight for sorcerers, who usually discover their power by accident, in a fit of anger or frustration. Since the one unbreakable rule of the universe is "you can't unmake something with sorcery, and if you try, the universe unmakes you", most potential sorcerers don't survive the discovery of their powers.
Also done literally when Silk tosses Brill off a mountain, forcing the Dagashi to try to learn how to fly before he hits bottom. Does bouncing count?
In Mistborn, Allomantic powers are activated by "Snapping", which involves some form of trauma. Most nobles give their children a savage beating at some point in their life, hoping they're latent Allomancers. Kelsier was Snapped by the death of his wife. The best way is to experience "mist-sickness", which only affects latent Allomancers and by design causes just enough harm to Snap them.
Several times in Katheryne Kurtz Deryni universe someone discovers that s/he has Deryni (magic-user) blood in an extreme situation. Not all Deryni, even very powerful ones, are Healers; but those who are often first discover that they have that power when someone is hurt and there is no Healer available.
In J. R. R. Tolkien, magical powers are often unlocked by an intense need to use them.
In The Secret Texts Kait discovers she can Shift into a flying form this way. Specifically, jumping off a tower.
Obligatory Discworld reference: Archchancellor Ridcully once disputed Ponder's notions about evolution using this trope, proclaiming that nobody's ever seen a lizard evolve into a bird to save itself after falling off a cliff.
The Vampire Academy character Lissa Dragomir had her spirit powers (which includes the power to bring the dead to life, at the possible cost of her own sanity) when a car crash kills her parents, brother, and best friend, while leaving her alive. In the moments after the crash, she unintentionally, brings her friend back to life, though at the time she does not realize that she was actually dead.
Richard's magic, a lot of the time, in The Sword of Truth series. Being a War Wizard, Richard's magic tends to do whatever the plot requires of it, without Richard understanding what he's doing, or how he's doing it.
An odd varient in the Knight and Rogue Series. When Michael is tossed off a cliff his magic activates on his own and saves him. Despite not wanting to die, he stops it the moment he realizes what's going on. (Fortunately, he's only a few feet from the ground at this point). The only time they don't manifest when his life depends on it is when he's desperately trying to put out a fire.
In Septimus Heap - Darke Septimus must try the Flyte spell without its charm in order to escape from Dungeon Number One, and succeeds at it.
In the Wearing the Cape verse, breakthroughs usually occur as the result of a life-threatening or traumatic experience.
Live Action Television
Nathan Petrelli from Heroes discovers he can fly when he unconsciously rises into the air while his car is being shunted from behind by employees of a crime boss he is attempting to prosecute. This happened completely against his will; without him in the driver's seat, the car crashes, paralysing his wife from the waist down and leaving him with lasting guilt about his wife's condition.
Similarly, Claude attempts to help Nathan's brother, Peter, control his power-stealing powers by throwing him off a tall building, hoping to trigger the flight power he'd mimicked earlier from Nathan. In a unique subversion, while Peter's flight power is not triggered by the attempt, the regeneration powers he took from Claire Bennet are triggered when he dies after crashing and being impaled on a cab.
Similarly to Highlander above, in Kamen Rider Faiz, certain humans that are genetically predisposed to evolve into higher forms have no idea that they have the ability unless an early death kickstarts the process.
Paige's first use of her teleportation power in Charmed was to escape her parents' car as it crashed and exploded (discovered through the magic of Time Travel).
Her first use of her healing power came when she had only three options: orb out (exposing herself as magical in front of cameras, police, and civilian hostages), let her boyfriend Henry die right in front of her, or figure out how to heal (which is much less obvious as visually it's just a bit of light, and the wound didn't heal all the way as to seem suspicious). Naturally she was glad to discover that the third option was possible (as before she begins to heal him she had no idea that she could).
In the Nickelodeon remake of The Tomorrow People, Jade spends much of her series hanging out with Adam and Megabyte and wishing she could be a Tomorrow Person. Her powers are revealed when she saves herself (and her crush Megabyte) from an exploding boiler room.
On Fringe, David Robert Jones subjects Olivia to a series of tests for telekinetic ability, including a game where you make lights go off with your mind. With the Bishops' help, she fakes the test. She later finds a bomb attached to a skyscraper that will take out half of downtown Boston unless she can beat the same test for real.
On Sanctuary, Tesla's "experiments", a group of kids whose DNA he mutated so they would, as part of a very complex and convoluted end-game of his, become Vampires under his command in 30 years, turn into very powerful Vampires (30 years ahead of time) when they're killed, because the gene was designed to, above all else, focus on self-preservation.
See the video to "Ich bin wieder hier" by Bluemchen for a literal example: Jasmin Wagner's character falls off an airship and grows wings.
According to the background for the tabletop role-playing game Aberrant, the first recorded superhero following the Space Station Galatea's explosion was a firefighter whose flame-manipulation powers kicked in when he was trying to save some kids from a burning bus. Likewise, the "eruption" of several other Novas in the setting usually comes about as the result of a massively emotional experience, such as a near death experience. Given the celebrity associated with being a Nova at this point in history, a lot of people often try to kick-start powers of their own through such experiences; the results are often unpleasant and messy, to say the least.
Aberrant is unusual this way; the moment of becoming a Nova is similar to exposure to LSD, in that the results are dependent on the personality of the individual and the circumstances under which it occurs. In consequence, Novas demonstrate this trope by their very nature.
In the story of the Magic: The Gathering trading card game, those with the "planeswalker spark" can become Planeswalkers, powerful, immortal mages (representing the player in the game). To become a Planeswalker, one must "ascend", which involves great stress and usually horrendous death — the most famous example, Urza, was literally blown to atoms before ascending.
The Eberron novel The Grieving Tree had Ashi develop a mark to defend her friends from an angry dragon.
Deconstructed in the Mutants & Masterminds setting "Paragons": it's common knowledge that superpowers occasionally manifest this way, so a common cause of death is idiots attempting to invoke this trope by e.g. skydiving without a parachute or setting themselves on fire. Worse, once in a blue moon it works, which means that someone who is suicidal and/or not particularly bright now has superpowers, and moreover, everyone else has renewed encouragement.
In both Mage: The Awakening and its predecessor Mage: The Ascension, Mages tended to Awaken under life-or-death situations, or at least situations of incredible duress. Of course, many mages still end up dying shortly after Awakening anyway, since they tend to lose control of their powers or get careless and start eating a Paradox buffet.
In exalted, people tend to Exalt at a moment when they are in dire need of a boost of heroic supernatural power. It's supposed to be fated, but considering how many things muck about with Fate on a fairly regular basis, not even the Sidereals can always figure whose life or death situation will end up resulting in Exaltation.
The Lunars get a weird variant on this, seeing as they usually Exalt after managing to survive a life-or-death situation.
In Brave New World superhero rpg, superpowers are only ever known to manifest as the result of near-death experience (and the books even mention that it is not known how many people develop superpowers that do not allow them to the survive the life-threatening experience that triggered them).
The timeline for the GURPS International Super Teams roleplaying worldbook cites several such metahumans, including two caught in a nuclear bomb test in 1951, a girl whose rapist tried to burn her alive, and an early-1970s illicit American military program to "destruct-train" draftees in order to force a few metahumans out of their numbers.
The second Knights of the Old Republic applies this trope to the player character character, who learns on-the-fly to survive extremely deadly situations, such as poison attacks.
The Persona series uses this trope for the main characters of each game, usually by having them attacked by Mooks. Innocent Sin does it differently; the main characters all awakened their Personas at different times, and it's not Mooks they were in danger of.
Persona 3 uses this as a game mechanic, and it's symbolic.
Persona 4 subverts this with most of your party members. While the Protagonist still has his classic "Per...So........Na..." invocation scene, his powers were awakened by Izanami at the start of the game, the source of the rest of your party's powers is the very same thing that would have caused the Die or Fly reaction in the first place.
In Arc The Lad, Kharg's affinity for magic awakens when he is about to be executed by firing squad.
The player has to do this in Steel Battalion. No training, no tutorial, just the imposing controller and a complex manual. Good Luck!
In Fate/stay night, the protagonist Emiya Shirou first uses most of his abilities when protecting himself or, more usually, someone else, from immediate death. The first example is on the third day, in which he easily and instantly uses a perfect strengthening magic, which he normally has a less-than .01% success rate on with an hour to practice.
The Lord of the Rings: The Two Towers throws you right into the fray after the lengthy unskippable intro.
Evo Search For Eden does this in the age of dinosaurs, and quite literally at that. After climbing to the top of Mt. Brave, you are given a choice to jump off or leave. Jumping off results in an evolution... you become a pterodactyl.
In Final Fantasy XIII, when a l'Cie falters in his or her resolve, they may be challenged by their own power in the form of an Eidolon. Failing an Eidolon's trial is guaranteed death; overcoming the trial grants the l'Cie the ability to summon the Eidolon to assist them. Eidolon battles tend to be That One Boss.
In the backstory of Nine Hours, Nine Persons, Nine Doors, Gentarou Hongou believed that people who have minor psychic abilities (such as communicating telepathically through the morphogenetic field) could unconsciously develop and increase these abilities if faced with emotional trauma. To prove this theory, he kidnapped nine children and forced them into a Deadly Game. Gentarou was right, but he realized too late that his 'subjects' could use their newfound power to get revenge on him.
Happens to Terinu when his Bion abilities activate when he's drugged and kidnapped.
A more literal example occurs in the current One Question storyline, as Ranu falls off a building and his wings suddenly appear. Unfortuantely he needs some tutoring to learn how to use them...
Even before that, she tried it in a much more literal sense with Tavros. He didn't fly, and wound up paralyzed from the waist down for his trouble.
In El Goonish Shive, Grace first discovers how to create legion forms when she is under pressure to change to a form strong enough to maintain her telekinesis without passing out in order to save Ellen and Nanase's lives during the fight with the Omega Goo as seen here and on the next page.
Played with and lampshaded in The Dreamland Chronicles. While taking flying lessons, Alex asks if the lessons involve him getting thrown off a cliff. The teacher asks why on earth he would do something so risky. After exhausting all of his other ideas, the teacher does throw Alex off the cliff, only to realize that also isn't going to work, so he reminds Alex of his promise to his Love Interest. This motivates Alex enough to save himself and learn to fly.
In Pacificators, this seems to be how Daryl learns new tricks. When her platoon were stranded out on the ocean with no food supplies, she learned how to flare her staff's orb brightly. Later, when faced with gun-toting Preservers, she became the first person to discover how to use solar power and used it to sting the enemies.
Gypsy gained her powers when she and her little brother were victims in a drive-by shooting. Her powers allowed her to survive. Her little brother was less fortunate.
Aurora was caught in an uncontrolled fusion reaction. Rather than be vaporized, or die of radiation poisoning, she became a living, human-shaped fusion reactor.
White Rabbit gained her powers in a car-wreck that almost killed her and her infant son.
In Alex Reynards online novel "Dangerous Lunatics", Holly discovered her near-immortality-level Healing Factor through attempting suicide... six times.
It happens to Tennyo in her origin story in the Whateley Universe. She wakes up and finds herself a prisoner, and finds she now has energy powers. When mutant assassins come after her (to send a message to her superhero parents), she finds out (in the nick of time, natch) that she can create an energy sword, and that she can fly.
Even closer to the trope, Jade's powers first manifested to save her from being possibly beaten to death by her abusive father. Die or fly indeed.
In Phaeton this is one way to trigger manifestation in the youngest of people.
In Worm, all parahumans get their powers in a Traumatic Superpower Awakening, which can include one of these; Brandish and Lady Photon, for example, got their powers when they were about to be murdered, and Grue got his powers during a violent fight with Aisha's abusive stepfather.
Not that parahumans can't get this. Some of them have a second trigger event, which alters their powers. Grue, for example, had the power-draining effects of his darkness enhanced and gained the ability to copy others' powers with it, alongside more minor changes in how the darkness functions. Some parahumans had their second trigger event essentially at the same time as their first.
In Ben 10, this is how Ben discovered his Wildvine form. It's downplayed in that Wildvine wasn't particularly useful that episode, though the form was able to handle the immediate threat.
Danny Phantom busts out his Ghostly Wail to defeat his future self when it looks as though he's going to be defeated and everyone will die.
Technically, he first got it when he was ganged up by some really angry ghosts, but the Ghostly Wail did serve as a hidden weapon for his final battle in the episode.
In "The Avatar State," an Earth Kingdom general attempts to induce the Avatar State by putting first Aang, then Katara in danger. It works.
Also, in "The Puppetmaster", Katara learns Bloodbending when her Evil Mentor Hama takes control of Aang and Sokka and was about to make Sokka stab Aang.
Happens in episode 16 of My Little Pony: Friendship Is Magic, when Rainbow Dash finally manages to pull off her Sonic Rainboom technique to save her friend Rarity and her idols the Wonderbolts from plummeting to their doom after Rarity's wings failed and the Wonderbolts were knocked out in their attempt to rescue her.
This is pretty much how Fluttershy's ability to fly at high-speeds works. She can match Rainbow Dash's flying speed, at least for brief moments, but only when it's absolutely necessarily and seems to be a fairly poor flyer at other times.
Outright fails to work in Sleepless in Ponyville where the flightless pegasus Scootaloo still can't fly even when facing a fall to her certain death, it takes the timely arrival of Rainbow Dash to save her.
Some people believe that the best way to teach children to swim is to throw them in the water where it's deep. These people are wrong. Awesome way to teach children to thrash in water, develop a phobia, hate water/swimming/you or drown, though.
Though there are those people who think it worked well enough for themselves.
Averted in the case of some birds. The mother bird pushes the chick out of the nest, and the bird's die or fly instincts kick in, often resulting in the bird flying. However, the mother bird swoops down to catch the chick if it doesn't manage to take flight in time.
When faced with life or death, the human brain goes into survival at any cost mode. This includes shutting downs strength restrictions that prevent muscles from tearing themselves apart and releasing endorphins to prevent the sensation of pain. Net result: you can lift a helicopter for several seconds.
Additionally, sometimes the brain will bypass the normal functions resulting in amplified senses and reflexes.
Deconstructed with many Darwin Award winners, and "breatharians."