Beyond the Impossible/Western Animation

The medium of Western Animation is such that literally anything is possible. Beyond The Impossible, in this case, refers to those rare actions and events that do not conform to the previously established rules of its universe. Generally, the more realistic a work is, the greater the likelihood that something going Beyond The Impossible can be found. Cartoons like Looney Tunes would be exempt from this trope, because the characters and settings follow no rules except the Rule of Funny (a rule which cannot be broken, only ignored).

"Jumba: No. When something is hydrated there is absolutely no way for it to being dehydrated.
 * In Avatar: The Last Airbender, Earth Benders repeatedly demonstrate that they cannot bend metal. Magic a Is Magic A is so strong with this one that an entire episode was based on earth benders as POWs in a metal prison. This trope comes into play near the season two climax.
 * The Legend of Korra: "Its not a full moon...how are you doing this!?"  A panning shot later confirmed that the moon was indeed only a cresent.
 * Amon
 * My Little Pony Friendship Is Magic is rather cartoonish to begin with, and that's not accounting for the innate magical abilities of the ponies. Teleportation, flight, and walking on- clouds are all relatively common feats, and all of the characters have their moments where they defy physics. Pinkie Pie takes this to extremes, but she generally doesn't do anything outright impossible... except for the one time she appeared in a mirror without being in the room. That was weird.
 * Before Rainbow Dash performed her first Sonic Rainboom, the stunt was considered by all to be impossible, an "old mare's tale". When she managed to do it, she went Beyond the Impossible, at least in the eyes of the rest of Equestria. For that matter, considering that calculations have suggested Rainbow Dash is pulling Mach 10... It's just Beyond The Impossible, period.
 * At the very least, a Sonic Rainboom requires her to break the sound barrier. Rainbow Dash is Equestria's only supersonic pony.
 * In the episode "Sisterhooves Social", Sweetie Bell, Rarity's little sister, burns juice and liquifies burnt toast while trying to make breakfast in bed for Rarity. Her parents not only seem to like it, but also imply that her mother actually taught such school of cooking.
 * In the episode "A Friend In Deed", Pinkie Pie has an Imagine Spot done in felt as she runs through her checklist of friend-making activities. After coming out of the spot, she resolves to complete her list, and punctuates it by holding up a green felt checkmark from her Imagine Spot...
 * Billy from Adventure Time. While the show has a habit of doing this anyway, Billy's backstory had him defeat the Ultimate Evil and literally PUNCH AN OCEAN TO DEATH.
 * Also, HE FOUGHT A BEAR!
 * Finn popped a bubble he had made into a black hole with a four-dimensional sword despite in show and real life logic and physics saying otherwise.
 * In Wakfu, Nox, the main villain of the first season, is a powerful Time Mage who has been alive for over 200 years, collecting life energy and feeding it to a powerful magical artifact called the Eliacube, trying to accumulate enough energy to turn back time in order to undo a mistake which caused the death of his family. He has slaughtered countless people and entire civilizations for this purpose alone, despite being warned that doing so is impossible, even for a Time Mage, and could instead result in reality being destroyed. In the end, he manages to achieve his energy goal and actually succeeds in turning back time by 20 minutes.
 * Transformers Alternity Megatron's Tesseractal Swords are blades of infinite length. "Physical space is not an obstruction."
 * Ben 10: Ultimate Alien has a scene where Gwen slaps Humongosaur out of a drug-fueled rampage. She can canonically beat substance abuse out of people.
 * At one point in Bionicle Jaller sets Mantax ablaze on the ocean floor. Elemental Rock-Paper-Scissors is important in the series so its Handwaved with the Wizard Did It rule; he has power over fire, and if he wants fire underwater, he can do that (not easily, but still...).
 * Played for laughs in Lilo and Stitch: The Series. The duo have failed to reform 627 in the usual way, so they ask Jumba, resident Evil Genius and 627's creator, if they can dehydrate him back into pod form.
 * Played for laughs in Lilo and Stitch: The Series. The duo have failed to reform 627 in the usual way, so they ask Jumba, resident Evil Genius and 627's creator, if they can dehydrate him back into pod form.

TV Commerical: Have you ever wanted to dehydrate something? Now you can!"

"Professor: Nothing's impossible! Not if you can imagine it!"
 * They place an order and the device works.
 * Jonesy from Sixteen can get a tan from the mall's florescent lights. His explaination: "The key to a good va-cay is all in the mind ." Nikki shouted how impossible this was but the tan was there so there wasn't much she could do about it.
 * Men in Black have a Freeze Ray that can freeze fire.
 * Teen Titans: Cyborg once got in a Brawler Lock with an insanely strong robot who was working at full power. Cyborg won by going farther than full power. His meter was at around 160% before it exploded. This was in fact the Aesop of the episode: Cyborg believed it was impossible for him to get any stronger/faster/better etc because "I'm a robot; my limits are built in." His human half allowed his mechanical half to perform better than what should have been possible.
 * Futurama: Many Professor Farnsworth's inventions involve screwing logic. For example, the Planet Express ship doesn't fly, it stays put and moves the universe around it.