While she's no pushover before this, her first jaw-droppingly kick-ass moment has got to be when she defeats the entire Sound Team by herself, killing all three of them without flinching until the threat to her teammates is over. Then when Sasuke is possessed by the Curse Mark, she takes a strike to the chest, which snaps him out of hispower-trip.
Using the Substitution Technique with only a moment to spare to switch with Sasuke, taking Itachi's Tsukuyomi full-force.
Defeating Kidomaru, with Kiba and Akamaru backing her up. And given that Kidomaru shrugged off Ino's Signature Move, it makes her triumph all the more savoury.
All the various stages of that two-chapter fight deserve mention, actually, including a meta-example in praising the author for constructing it so well despite that "the fight scenes are killing [her]".
Her fight with Muku during the exams in Kusa. Her opponent can seal a ninja's chakra; most ninja black out at that point, and the few that don't can't usually fight without chakra. Shikako stays conscious and uses her knowledge of sealing to activate her explosive notes without access to her own chakra, gains an edge in speed by disabling her resistance seal, again without chakra, and finally strangles him with her own hair until he loses consciousness.
Kakashi: "There are Jounin in the crowd that wouldn't have wanted to fight that match."
The next round after that, she faces Gaara. She loses, but she puts up an impressive show.
Impressive enough that Gaara uses his sand to bring her back to the stands.
For reference, impressive means: turning the flat grassland battlefield into a forest of stone pillars using a seal, recreating Deidara's bombs in the sand method using linked exploding tags, dropping a pillar on Gaara, sealing his sand and the Shield of Shukaku, faking him out using the Raijin no Ken and her chakra control indicator seal, using said chakra control to turn the water she had stored on her into a staff, and using a seal to turn the air into a barrier. Oh, and using her feet to set Touch Blast explosives that turned the City of Pillars into ruins.
Naruto curb-stomping Neji, during the Chuunin Exam Finals. Made even better because it came about as a result of Shikako mentoring him in a way which kept him interested, and raised his intelligence several notches compared to canon.
In Ino's fight against Temari in the Chuunin Exam Finals, she manages to disarm her opponent which - given Temari's reliance on the fan for her Wind-based techniques - leaves her weakened despite defeating Ino, and so she becomes easy pickings when the Invasion breaks out. Offset somewhat by Ino not preparing for her opponent being strong without her weapon, which leads to her being denied a promotion.
Shikamaru and Shino's fight in the Chuunin Exam Finals. Seeing two of the best strategists in the series duke it out in their incredibly subtle manner(s) is highly impressive, and barring Naruto and almost Shikako (who didn't even make it to the Finals, but was praised for her deductive reasoning), they're the only ones receiving promotions when all is said and done.
In the Sasuke Retrieval Arc, Hinata of all people pulls a Big Damn Heroes - and then uses her new move against Kimimaro in the process:
Hinata: "Protection of the Eight Trigrams; Sixty-Four Palms".
Followed by Lee, Naruto, and the Sand Siblings each making their own, in that order.
And reaching it's peak when Naruto, Sasuke, and Gaara kill Kimmimaro. First, Gaara pins him down with a wave of sand, then, Naruto and Sasuke recreate their Rasengan / Chidori clash from their canon fight in the Valley of the End, but with Kimmimaro between them.
During the Stones of Gelel movie, Shikamaru fights back against Gelel itself when it tries to use Shikako as a host. And it works.
Gelel:You would fight a god?
Shikamaru: Yes. Give me back my sister.
A Sunshine Sidestories chapter reveals Shikako's mission history to the other Kages. Case in point, her history of A-ranks (and one S-rank) along with her Genin status and the fact that it's not even been a year since her graduation from the academy has the Raikage convinced she's a Jounin plant.
Tsunade: It's hardly my problem if your Genin don't match up to ours.
In round 2 Shikako faces a Grass ninja named Muku, who is ''not'' a genjutsu specialist as assumed, but a sealing specialist who seals her ability to use chakra. Due to her experience without chakra Shikako plays dead to lure him close for a surprise attack, endures a kick that breaks her arm, uses her own blood to booth remove her resistance seals for a speed boost and prime her explosive seals, and finishes by choking him out with her own hair.
In round 3 Shikako fights Gaara. She begins by using her prior terrain knowledge for a seal that brings up a forest of stone pillars for her to maneuver around. Then she peppers him with kunai that have miniature explosive seals attached, which get into his sand the same way Deidara's clay did and explode. After another short skirmish she drops another giant rock on him and pulls out the Sword of the Thunder God. She fakes him out after launching two attacks, seals his Shukaku Shield, throws water at him in imitation of a water element jutsu, explodes the stone forest with Touch Blast seals she'd put down through her feet, and finishes up with an air barrier, before he catches her and she loses. It takes her a minute to realize that the applause aren't her heart roaring or genuine thunder.
By the chapter 98, Shikako's awesomeness had reached memetic status. She's promoted as Special Jounin just days after declared chuunin. Nothing compared to Gaara who went straight being Kazekage, but still.
Tsunade: And Hatake said Naruto was the Konoha's most surprising ninja.
A meta example in chapter 104 The Mission Desk Ninja's become Ascended Fanon.
When a movie villain shatters Shikamaru's arm, Shikako repays the damage tenfold.
To elaborate, Shikako kills one of the enemy, gored on Heijomaru's horns, as part of their retreat. After securing everyone on the boat she goes back to the castle alone. She sneaks in using flash bombs to draw away attention and confronts the lead enemy alone, using a monologue to distract from her shadows. She Shadow Possesses him into destroying one of his own arms, and in the following clash cuts off the other and seals it away before appearing to retreat. After a few minutes of spying she kills him and explodes his teammate within an inch of her life before letting her run.
One reviewer pointed out that Shikako single-handedly achieved what originally took Rock Lee going all out, Sakura's strength and tactics, and Naruto's assisted Rasengan to achieve.
In chapter 120 Shikako and Kiba happen upon 3 foreign Anbu agents who have kidnapped some children. The first dies from a combination Shadow Possession and Tunneling Fang, Shikako pins down and skewers the second despite his Body Flicker-ing by letting him stab her in the back and turning to shadow, and then gets around the third's body hardening jutsu by snapping his neck.