In "Reptiles in the Rose Garden," King Koopa takes over the entire United States in 5 minutes by warping the White House to the Mushroom Kingdom and instating Kootie Pie as Empress of America, all to make her happy for her birthday.
The climax of "The Ugly Mermaid" where Mario overcomes his fear of water (instilled after almost drowning) to save Luigi, the Princess, and Toad.
Both the Mario Brothers get one in the song segment, where they take a net, fill it with Jelectro, and throw it at the Doomsub.
Earlier, Koopa sends a wave of Boomerang Brothers to attack Mertropolis. Everyone works together to take them out.
Holly Mackerel saving Mario from drowning in "The Ugly Mermaid." Then, Toadstool, Toad, and Luigi break the concrete block he's trapped in and get the water out of his lungs.
Luigi scaring the Boos in "Misadventures in Babysitting."
Koopa got one in "Never Koop A Koopa" where everyone was captured and at the mercy of Bob-ombs. The only reason he lost was because Cheatsy decided to cheat him out of ruling the kingdom.
Princess Toadstool got one when she scribbled onto the scroll instead of signing it, figuring Cheatsy wouldn't bother to look at it before running off to show Dad.
Cheatsy tricking Mario by disguising Kootie Pie as a human in "The Beauty of Kootie."
The Mario Bros. pay them back by disguising Luigi as a handsome Koopa, distracting Kootie Pie long enough for them to undo their plans.
In "Reptiles in the Rose Garden," the heroes have been captured and are guarded by Chain Chomps, a Boomerang Brother, and a Fire Brother. Princess Toadstool convinces them to fight each other, and in the confusion they hold up their chains to get hit by the stray fire and boomerangs.
Any time Koopa refuses to get Kootie Pie what she wants. Special mention goes to the end of "Reptiles in the Rose Garden," where he orders her to clean her room, stomping the ground with such force that the castle starts to crumble.
In "Super Koopa", Koopa uses a magical pendant to use the Raccoon Tail, the Fire Flower, and Kuribo's Shoe at the same time.
All four heroes got one in "Super Koopa", where the Princess and Toad kept the Mario Brothers stocked with power ups to fight Koopa, who was also powered up.
The climax of "Do The Koopa", where Mario resists Koopa's mind control music by plugging his ears, then tackles him, starting a war for the Doom Dancer that culminates in it falling over the side of the ship and landing on an unfortunate Goomba.
Their infiltration of Dark Land was cool too, with all four heroes getting raccoon tails.
Bully's plan to rule the world in "Do the Koopa."
Even the one-shot characters have these moments. With the help of the Mario Bros., Crimewave Clyde not only stops the Koopa Kids from robbing the Mushroom Kingdom Treasury, he ties them up and blows up a part of the Doomship with a Bob-omb.
Clyde's Heel-Face Turn as a whole also counts. He even graciously returns to prison to serve his sentence.
The scenes in "Mind Your Mummy Mommy, Mario" where Luigi rigs up a steam-powered hot air balloon to invade Koopa's tower and get back Prince Mushroomkhamun's mummy case; it makes it even after running into a twister from Desert Land.
Once they get inside, Luigi then rigs the sarcophagus up for use as a sled when everyone's trapped in Koopa's tower. This is followed by a segment using the instrumental for "Mega Move" as they chase Koopa and his kids down the stairs, defeat Paragoombas with raccoon tails, vault over Chain Chomps, and escape by bouncing down the parapets and surfing onto water safely.
"Seven Continents for Seven Koopas" has Toadstool escaping captivity on her own and unclogging the pipe that was keeping the Mario Brothers blocked off from the Real World. She did this by coaxing a Bob-omb to explode in it. That took guts.
Toad even mentions the Princess can handle herself.
"Up, Up, and a Koopa" has the Princess and Toad using P-Wings to rescue Mario and Luigi and foil Koopa's anti-gravity scheme.