Meimi's magic tricks. According to Word of God, she's better than her own father... And not only she can both do his old tricks besides her own, but she proved capable of performing one of his newer tricks after seeing part of it once (it was a substitution trick she used to make Rina believe that Saint Tail is a man in drag).
This was awesome for Asuka Jr. too, for he managed to recognize the real Saint Tail in the middle of the copies.
The group of tuxedo-wearing dancing kangaroos from the prequel chapter is one of her strangest tricks... And one of the most impossible.
At the start of episode 21, she performed a Doppelgänger Spin with mirrors. With the copy being far too distant for any realistic mirror trick studied to do that.
She does it again later in the episode. This time the awesomeness is for Asuka jr.: he deduced which one was the real Saint Tail (he couldn't tell the difference like he did with the Parade, but could guess it).
Another trick first used by Genichiro: in-door snowing. Complete with cold. Then the snow becomes something else (confetti in Genichiro's version, the flower named snow drop in Saint Tail's).
In episode 7, Asuka jr. actually succeeded in surprising and grabbing Saint Tail. She escaped with an unwitting assist from Rina, after being pranked by Saint Tail while in the surveillance room, attacked with tear gas without knowing she was already in Asuka's grasp....
In the same episode, the director of the museum targeted by Saint Tail was complaining to Asuka sr. about Saint Tail successfully stealing a valuable archaeological treasure, and asked him how the police was going to take responsability.
Asuka sr.: "Ah... It's a nice painting. Don't tell me this is an imitation, too?"
Asuka sr.: "I've already investigated. I hear your Dagger of Yato is a genuine replica."
Rina discovering that Meimi is Saint Tail in episode 8, and not letting herself be fooled by Meimi's attempts at disproving her findings (at least until Rina touched Saint Tail's moustache in episode 10).
Episode 9 sees Saint Tail stealing a wedding dress while the model is wearing it. She replaces the dress with a bulky dinosaur costume. Then she covers her escape by tossing dozens of bouquets, leading the girls of the audience to catch them and obstruct Asuka Jr.
In chapter 10, Saint Tail finally convinces Rina she's not Meimi. It's mostly a Funny Moment due it involving faking being a man, but given how Rina had quickly saw through Seira faking being Meimi while Saint Tail appeared somewhere else in the previous chapter...
The anime version makes this even better by showing where the switching magic used to pull it off (by replacing Saint Tail with the male moustached substitute) came from: a couple days earlier, her father had shown Meimi part of that trick... And she reconstructed it.
That, and Genichiro's version: he switched himself with Eimi while holding Meimi's hand. Meimi didn't notice until she opened her eyes and saw she was now holding her mother's hand...
Rina actually catching Saint Tail. Sure, then she escaped, but Rina had actually grabbed Saint Tail and almost put her in a submission hold.
Saint Tail's apparition in episode 13 to steal Princess Rosa's Mirror: she appeared on a decorative chandelier while filling the room with the flowers named after the mirror's original owner, Princess Rosa.
In the anime-only episode 14, Saint Tail hacked in a video game console not connected to internet (that was also before internet use became widespread). She then stole a bicycle by making it fly in a Shout-Out to E.T..
Episode 15 has the playful and non-indicatively named dog Little facing three jewel thieves. As soon as Saint Tail eliminated the gun from the fight, Little pulverized them.
In episode 20, a professor Hyuga swore he'd use his advanced technology to reveal Saint Tail's identity. Saint Tail defeated his technology with magnets.
Episode 23 reveals that Saint Tail is becoming The Dreaded for the town's crooks, because she got half of them arrested. We're also shown a montage of what had been multiple Offscreen Moments of Awesome, in which Saint Tail caused the arrest or captured some crooks and left them for the police.
In episode 25, the police brings in Kaede Kitamura, a super detective from Tokyo, to arrest Saint Tail, and, thanks to the use of cars and electronic trackers, she nearly catches Saint Tail multiple times (at least until Saint Tail notices the tracker and dupes her into trying to arrest Rina). Asuka jr., temporarily off the case, comes much closer using only a bike and his brain, and only fails because Kitamura gets in the way to the point of having him forcibly locked up. For obvious reasons, Asuka jr. is back on the case by the end of the episode.
When Kitamura tried to arrest Rina, the girl fought back-and matched the elite officer Judo throw for Judo throw for a few minutes, at least until her uncle the mayor got over the shock and stopped the brawl. And Kitamura had the surprise effect on her side.
In episode 28, has the leading pair exchanging awesome points. Asuka Jr stages a trap that combines the local environment with what he knows of Saint Tail's showmanship. However, Saint Tail anticipates this and ties up the cops responsible for springing it. When sprung, it succeeds in trapping her but only because Rina was coincidentally in the right place to do so. Then Saint Tail's latest "client" shouts for Asuka Jr to release her, which he does, reflexively.
In the episode 29-30 two-parters, Yabe, a thief hired by the mayor of the town of Sakuraoka, sends a fake Saint Tail warning note to announce he'll steal a crystal sculpture borrowed from Sakuraoka, prompting Saint Tail to try and steal it first to prevent Yabe from getting it. What does Asuka jr. do? First he actually captures Saint Tail after she had defeated all the guards, then, when Yabe steals the sculpture while he was busy, he leaves Saint Tail and chases him, even jumping on his car's roof, and staying there until his hands were numb. He still managed to see where he was coming from.
Later in the two-parter, some awesomeness for Yabe for catching Saint Tail completely by surprise and capturing her. Not that they could keep her captured...
After that, Yabe and the mayor try and escape. It takes them a while to notice that Asuka jr. has sneaked on their car while they weren't looking... And they don't notice Saint Tail chasing them until she made the car fly. And immediately after that, Asuka jr. giving Yabe all the kicks in the face he deserved.
Pandora casually confirming Saint Tail's identity with a bit of scent-based hypnosis.
Immediately followed by Saint Tail completing her caper with a flame-based illusion so realistic that Pandora was crying in terror and didn't even notice it wasn't hot.
We see Rosemary's hypnotist skills in action. The previous episode we saw her adopted daughter and she was good, and in another episode we saw Saint Tail and Genichiro and they were comparable to Maju, but Rosemary is just in another league. Poor Asuka jr. was knocked out for hours, and didn't recover until Rosemary made him.
It turns out that Pandora is even better at hypnotism than Saint Tail and Genichiro. After all, they can't conjure an hallucinatory army of skeletons on a whim.
Saint Tail's retaliation: she summoned wind (with illusory feathers while wearing equally illusory angelic wings for good measure) to dispel the hypnosis and take all the powdered lavender essence out of Maju's trinket, essentially disarming her.