Impossible Task Instantly Accomplished

"Doctor: Ah, the security protocols are still live. There's no way to override them; it's impossible!

River Song: How impossible?

Doctor: Two minutes."

- Doctor Who, "Flesh and Stone"

This trope is when someone receives an extremely difficult task which should take them a long time to complete, if at all, but they finish much sooner than anyone expected. This task doesn't need to come from someone else; maybe they challenged someone to a contest of some kind not knowing their opponent was the world champion at that particular activity. The important thing is that the person performing the task not only succeeds, but greatly surpasses expectations.

Often a Crowning Moment of Awesome. Can overlap with Achievements in Ignorance. Compare Impossible Task, for when the task is merely completed, possibly even just by technicality. Also see We Do the Impossible for characters who are likely to accomplish this kind of thing.

Anime and Manga

 * Dragon Ball: Master Roshi took 50 years to develop the Kamehameha Wave, and is first seen using it to extinguish a burning mountain. He levels the mountain, but that's not the point. The point is, Goku performs a weaker version of it almost immediately after seeing this feat.

Film

 * Iron Man: Tony Stark is captured by would-be conquerors, and forced to build a Jericho Missile, which he designed. He instead designs a miniature Arc Reactor, builds it, designs a suit of Powered Armor, builds it, and escapes. All in just 3 months.

Literature

 * Discworld:
 * The Last Hero: Leonard da Quirm is ordered by the gods to paint the ceiling of a massive chapel in Ankh-Morpork with suitably epic art, and is given 10 years to do so. Everyone present reacts as though this is too short a time. A week later, he has finished painting the chapel with
 * Going Postal: At the climax of the book, Postmaster Moist von Lipwig has challenged the clacks system, which is a form of sending messages over long distances with flashing lights(used as a stand-in for the internet in Discworld), to a race. Whoever can deliver their copy of a message to it's destination on the other side of the Disc first, wins.
 * The Last Continent: Rincewind, with a bit of help from a talking shapeshifting kangaroo, completely shatters the record for speed sheep shearing, having never tried it before.
 * Interesting Times: Rincewind is running away from his latest pursuer so fast, he ran over the surface of a fish pond. But he isn't the recipient of this trope this time. That honor goes to Pretty Butterfly, who caught up with him.

Live Action TV
""I'm Dr. Rodney McKay, alright? Difficult takes a few seconds; impossible, a few minutes.""
 * The Doctor of Doctor Who does this fairly often. On one occasion, he restored all of time and space, within about two thousand years. That may not sound like a short time, but considering that this is the biggest task anyone could ever be given, I think it belongs here.
 * On Star Trek the Original Series, Kirk often asks Scotty to perform impossible feats of engineering, generally involving completing repairs in a much shorter time than Scotty claims that he needs. He always comes through. In the third movie it's revealed that Scotty always multiplies his estimates by a factor of (at least) four, so that his tasks only seem impossible. Geordi La Forge on The Next Generation may be a better example of the trope. In one episode, when a visiting Scotty learns that the estimates Geordi gives Picard are actually accurate, he asks, horrified, "How do you expect to be considered a miracle worker if you tell them how long it will really take?" And yet Geordi still manages to pull things off just in time, and well under the given estimates.
 * On Stargate Atlantis, McKay uses this as a Badass Boast.

Mythology

 * Some of Heracles' twelve tasks from Greek Mythology were accomplished within ridiculous time limits, particularly the stables.

Real Life

 * One of many stories about mathematician Carl Friedrich Gauss's early life involves a lazy teacher assigning his class the busy work to add up all numbers between 1 and 100. Within a few minutes Gauss presented his answer of 5,050. He'd thought about it a moment, and realized that it's a set of 50 pairs of numbers that add up to 101.

Tabletop Games

 * Very high-level Dungeons and Dragons characters (especially at epic levels) can pull this off. For instance, creating a masterwork sword within seconds, or taming a powerful wild beast within a minute.

Video Games

 * Mass Effect: Pretty much everything Commander Shepard does. Suicide mission to Ilos, which features The Dragon, the Big Bad, a Nigh Invulnerable dreadnaught backed up by an entire fleet of geth? Done. What's next? Oh, a suicide mission that takes the previous accomplishment Serial Escalation? Done, possibly without losing a single person. As Shepard can say, "They call it a suicide mission. I intend to prove them wrong." And he does. And makes it look easy.
 * Kingdom Hearts II: Sora destroys 1000 heartless in hardly any time at all. The awesomeness of this is dampened as all of said heartless had an attached Reaction Command which allowed the player to kill many at once.
 * Touhou: Kaguya's spellcards are all themed around this trope. In-game, that means you have to defeat her (fairly difficult) spellcards. Of course, if Kaguya is involved, "instant" and "eternity" might as well means nothing...
 * And then there is Youmu, the sole gardener of Yuyuko's impossibly vast garden in the afterlife...
 * The Legend of Zelda: The Wind Waker: The Link in this game has no connection to the Hero of Time from Ocarina of Time, but manages to get wrapped up in Ganon's plot after his sister, Aryll, is kidnapped. He then proceeds to power through his Butt Monkey status, wield the Master Sword, repower the degraded Master Sword, earn the Triforce of Courage and the title of Hero of Winds, and win a Duel to the Death with Ganon. All in a matter of weeks, if not days.
 * Also toyed with in-game during the pirate ship minigames. The pirate to whom you are swabby challenges you to complete tasks that took him months, if not years, to accomplish. Skilled players can often complete this tasks on a few, if not a single, attempt.

Web Comics

 * Drive: The nameless maker was told to build a device which could isolate and contain a single quark, with the meager materials provided, without food, within a week. He could have spent an extra day making it really impressive, but he wanted a sandwich, so he finished in an hour.
 * Saturday Morning Breakfast Cereal: According to this strip, if sex didn't exist, we'd conquer heaven in two months.

Western Animation

 * Eek the Cat: Eek is sent to hell, and forced to clean out an infinitely large litterbox. He finishes in three seconds. Played for Laughs.
 * A core part of Phineas and Ferb. Hey, Ferb! I know what we're going to do today! Something that should take a crew of engineers months!
 * The show being what it is, this is lampshaded to the end of the world and back. Like when Candace asks them to fix her absolutely destroyed phone, Phineas points out it took almost a century to perfect the technology so it should take... 38 minutes.