Stitch quickly getting the X-Buggy back up after it falls down a ravine with Lilo inside. He dives down, catches the buggy before it hits the bottom, and climbs back up the ledge carrying the buggy in one hand/paw, all in a matter of seconds — and this was after he hesitated for a bit.
Lilo and Stitch going straight into a freakin' black hole in order to destroy it.
Stitch getting over his fears for his 'ohana's sake and taking down the shapeshifting green blob whose main purpose is to make people afraid.
Cannonball does a Big Damn Heroes moment when he jumps out of the sandcastle Stitch made and uses his powers to concentrate on Gantu, washing him into San Francisco.
The teamwork Lilo and Stitch use to capture Yin and Yang, using their combined resources that Jumba and Pleakley gave each of them to their fullest.
Yin and Yang are able to create islands when their powers are combined together. They are able to create an ecosystem from the ground up!
Lilo finds a way to save both the Earth and the Asteroid with the help of a few experiments and a rocket from Jumba's ship. Shows how smart she really is for such a young girl and taking charge.
Hämsterviel taking out Stitch with a plasma cannon. Double awesome as he had made the plasma cannon out of the playthings in his gerbil cage.
Stitch and 625's fight on top of Gantu's ship. Bonus points for 625 getting the upper-hand with some quick thinking.
More bonus points if you consider that his sudden competence is not even anAss Pull: 625 has the same skills and powers Stitch has. That wasn't just "quick", it was "faster-than-a-supercomputer" thinking.
Really, this is one of the few even matches in the show since while 625 is a coward, he's still got all the same abilities and skills as Stitch, so they are rather even either way.
Splodyhead and Stitch vs. Slushy, an epic five-minute battle that has everything from More Dakka fireballs and icicles, frozen tornados and giant monsters made of fire and ice.
Jumba: "Elemental evil genius experiments about to join in epic battle, and I forgot camera."note Funny thing about that comment, he managed to show a recording of that battle to the head of the Evil Genius Organization in "Ace".
Gantu trained four experiments into four very powerful and skilled combatants to take on Stitch. While he is able to beat them at full strength, they prove to be rather tough all together with them being the following: a plasma-shooting scorpion (617/Plasmoid), a laser-eyed triclops (609/Heat), a multi-tentacled thrasher (544/Thresher), and an alien with a hammer-like skull (033/Hammerface).
The Kaiju battle between the titular experiment and Stitch, including them using the things around them as a weapon.
Angel turning on Gantu and turning the experiments back to good after previously brainwashing them.
Also, before her Heel–Face Turn, Angel managing to undo a lot of Lilo and Stitch's work by doing said brainwashing on the experiments in less than a day.
Stitch knocking out a re-eviled Kixx with just an uppercut.
Lilo and Stitch saving Sample from a couple of alien enthusiasts.
"Bonnie & Clyde"
Lilo and Stitch taking down Bonnie and Clyde, who manipulated them for awhile and having them get locked up.
The fact that Jumba thought ahead with making a roof that is easier to fix. It is rather thoughtful and savvy on his part.
Lilo is able to, for a short time, use Stitch's powers to her advantage against Hämsterviel!Gantu, and later Stitch goes full on crazy when, as Pleakley, throws lemon bars into his eyes. Shows how improv can save the day.
Gotta give Jumba credit for this one. He's made an experiment that's so good at its job, it's almost scary.
Lilo, Stitch and the titular experiment are able to one-up the overlord Gantu in an alternate future where Hämsterviel has taken over the Earth. This includes taking on a new experiment (086/Clink) whose main purpose is to capture people.
Lilo becomes a full Action Girl when saving Stitch and Skip, as she is now able to use her adult form to its fullest. While it was only a short time, it showed how fast she can adapt.
Stitch saves Lilo's substitute teacher from the titular experiment's prank and later gets one up on him. PJ also gets special points for being able to even prank the hyper-smart Stitch.
Stitch being able to wake up on his own from Drowsy's sleep spell. Given how hard it was to awaken people from this sleep in its episode, that says a lot.
Retro is one powerful experiment: Not only can he manipulate the age of an item (turning them into an older version of itself), but it can apparently create ancient life forms out of their modern counterparts! He is likely the most dangerous of any o Stitch's cousins.
Lilo turned out to be right all along: the Night Marchers are real. Comes to Fridge Brilliance as the next episode on the production was a crossover with American Dragon: Jake Long. Thus explaining where magical beings are from.
While it's rather short, we get a fight scene between Jake Long, a 6-foot fire-breathing dragon with magical powers, and Stitch, a short but very powerful experimental lifeform made by aliens. The two are very evenly matched and even team up against Gantu later.
Pleakley turns Heckler's insults back at him by using it for his own comedy routine.
Nothing was more satisfying than seeing Mertle getting on the receiving end on some very deep-cut insults. She may be a kid, but for two seasons and several movies, this is rather refreshing.
Stitch holding his own against Shego. She's no pushover, even if he's a genetically modified monster.
Drakken gets one for himself, as he was able to make the perfect plan. If it wasn't for Kim and Lilo, he'd would have succeeded.
Lilo proves her worth to Kim with her own quick thinking, using Kim's grappling hook to free them. That is impressive.
Gantu taking on Robot!Mertle to regain his position as The Dragon.
Gretchen and Lilo using the relaxified Recess Gang and Stitch to get Lax to blast Hämsterviel's satellite with its relaxation blasts. Shows how smart the two girls are.
Ace's introduction is with a Heroic Fire Rescue that involves him making a makeshift parachute out of a curtain and saves a cat from the fiery building. For a "faulty" experiment, he's quite heroic.
Angel breaking out of her own containment capsule just by headbutting it, then doing the same to Stitch's capsule to free him, and then afterwards the two freeing Lilo and all the other experiments Gantu captured with the same method.
The whole series
The fact that Lilo, a little 6-7 year old girl who, up to that point, had an average life with her sister, is able to reform 600+ genetic monsters and get them to get into a normal life.