Trisana Chandler, or Tris for short is a walking talking example of Badass Bookworm at its best. A temperamental teen AND Fiery Redhead with a hot temper and the power to shoot lighting from her braids of hair.
Not just lightning. As of Shatterglass, she also binds winds, the power of the tides, and even earthquakes into her braids. By The Will of the Empress, she's added hurricanes to the power sources in her hair.
Daja managing to contain a forest fire and preventing it from killing an entire caravan of people.
Earlier in the same book, she pulls off a social CMOA by demanding that the Trader caravan trade with her directly for her mutant magic tree. Daja isn't about to take being treated like crap just because she's an unclean Unperson.
And she gets the caravan to listen to her by threatening to use her bad luck to wreck all their wagons.
At the end of Briar's Book, Briar follows Rosethorn into death to bring her back. The head of the Circle temple decides that the incident is best kept quiet.
Briar Moss. Knows street fighting and nerve points, and has plants that can rip you apart in seconds, as he demonstrates at the end of Street Magic.
Sandry can manipulate magic as if it's thread, and does so to bind the magic and possibly souls of the four main characters together. Because she didn't know it was impossible.
An earlier and smaller example is when she uses her heritage to force her table-mates to accept Daja, culminating in her throwing a girl's comment of "If she's (Daja) a lady, I'm a cat" back in her face by taking a pitcher of milk and pouring it deliberately onto the girl's plate while saying "If I say my friend is a lady, then you had best start lapping, Kitty."
Dedicate Crane & co. saving the collective hides of pretty much all Summersea (and Winding Circle to boot) from a really nasty disease via application of magic and The Good Old Scientific Method. Crane may be a jerkass of epic proportions, but damn it, he's a brilliant one.
Sandry's weaving of Unmagic in Magic Steps, using it in combination with her student's dance magic to capture the serial killers. It works, and when they take Paco hostage, Sandry responds by using the unmagic net to rip the killers to pieces.
Also from Magic Steps shortly before the events of the book her beloved uncle suffers from a heart attack. When she's barred from visiting, she calmly says "I'd like to see my uncle now." And causes every thread in the room (from curtains to clothing) to wrap around the guards as giant cocoons when they refuse to let her pass.
In Cold Fire, Daja walks through multiple building fires to save people. While her Required Secondary Powers confer some heat resistance, she's not immune and is still risking her life in a big way. The arsonist even thinks she looks like a goddess when she does this.
Evvy holding off a volcano in Melting Stones by convincing the fire spirits to put themselves into crystals.
The first time Sandry is kidnapped in Empress, Tris literally blows the doors off the room Sandry is being held in and bowls over the guards like ninepins. Briar saunters in casually after her.
The entire group breaking through a barrier meant to keep out invading armies and being held by the most powerful mage in Namorn.
Also from Empress, Quen puts Briar and Daja in his shields and mocks them, saying that he doesn't really need to defend himself against plant and metal mages. Briar turns his magic into vines to find the holes in the spells, Daja turns hers into wires and supports them, and they wrap him up and strip him of his power.
There's also Sandry's ultimate personal victory against the Empress. Berenene wanted to marry Sandry off to one of her favorite courtiers, thus keeping control of her estates and the money that comes out of them, and she wanted to keep the Circle in Namorn to serve her. In the end, Sandry signs over her lands, thus keeping control of them in Namorn, but she signs them over to Ambros, giving him the power to fight off the taxes Berenene had been using to financially squeeze him. By doing this, not only does she keep Berenene from having easy access to Landreg's money (as she would have if one of her court favorites had been in control), but she also gets herself and her friends out of Namorn, out of the Empress's clutches, and takes away any leverage Berenene would have had to bring them back. Compared to what Berenene had hoped for, keeping Landreg in Namorn is the bare minimum she could have gained. For someone who's renowned for always getting her way, that's gotta burn.
From "Battle Magic":
Rosethorn going on The Quest to take the Treasures to the Temple of the Sealed Eye.
Evvy managing to lock away the knowledge that she's being tortured for, and then she fakes being dead well enough that it fools the soldiers and a very powerful mage.
By the time the good guys are done with Weishu, he needs a whole cart to take back every treaty and agreement he signed with the God-King.