Daria/Awesome

The entire exchange with Helen and Ms. Li in "Arts n' Crass" is possibly the biggest and best of the whole series:

Li: Mrs. Morgendorffer, I'm afraid I have some rather bad news. Your daughter Daria appears to have been involved in an act of vandalism.
Helen: What?
Li: Mrs. Morgendorffer, your daughter collaborated with Jane Lane in the creation of a poster for our art contest.
Helen: Yes, I'm aware of that.
Li: We found part of the poster unacceptable, so it was altered prior to its entry. Unfortunately, someone defaced the poster while it was on display, and since your daughter and Miss Lane objected to changing it, I must assume that they were the vandals. I am afraid I'm going to have to take drastic action!
Helen: Wait a moment. You're saying the girls were against changing the poster, but entered it into the contest anyway?
Li: It was entered for them.
Helen: I was under the impression that participation in this contest was voluntary.
Li: It was, but your daughter refused to volunteer, so in her case, I made it mandatory.
Helen: All right, Ms. Li, let me make sure I have this straight: you took my daughter's poster from her, altered its content, exhibited it against her will, and are now threatening discipline because you claim she defaced her own property, which you admit to stealing?
Li: That's not what I said at all!
Helen: Ms. Li, are you familiar with the phrase "violation of civil liberties"?
Li stammers in terror...
Helen: And the phrase "big, fat lawsuit"?
Daria smirks.

- This was preceded by a Crowning Moment Of Awesome for the whole Lane family, in their own weird way: immediately before contacting Helen, Ms. Li tries to contact the Lane household. Trent is passed out (exactly as he was when the first call to the Lanes in the episode was made), and Amanda is ignoring the phone to focus on her craftwork (exactly as she was when the first call was made), leaving the phone to ring out completely. What makes this a Crowning Moment Of Awesome is that the inevitable result of the calls are so predictable to both Daria and Jane, they never bat an eyelid (and even exchange a smirk). Even though Jane can't count on her family to do anything, she can count on them to not do anything, which is something even Daria occasionally envies.
- To a lesser extent, Jake arguing on behalf of Daria and Jane's poster, comparing it to his penne a la pesto. Daria even thanks him for the defense.
Daria's graduation speech in Is It College Yet?:

Um, thank you. I'm not much for public speaking. Or much for speaking. Or, come to think of it, much for the public. And I'm not very good at lying. So let me just say that, in my experience, high school sucks. If I had to do it all over again, I'd have started advanced placement classes in preschool so I could go from eighth grade straight to college. However, given the unalterable fact that high school sucks, I'd like to add that if you're lucky enough to have a good friend and a family that cares it doesn't have to suck quite as much. Otherwise, my advice is: stand firm for what you believe in, until and unless logic and experience prove you wrong; remember, when the emperor looks naked, the emperor is naked; the truth and a lie are not "sort of the same thing"; and there's no aspect, no facet, no moment of life that can't be improved with pizza. Thank you.

Daria and Jane refuse to sell chocolate bars to a hypoglycemic woman who even fainted in front of them, and rather than being applauded for her good judgement by Principal Li, Daria is forced to do a reading at a local coffee shop that Lawndale High was raising funds for. To ensure that nobody ever made that mistake again, Daria read a violent right-wing spy story that whipped the kids into an anti-Communist mob and forced the coffee shop to shut down.
Brittney gets a quite surprising one in "The Daria Hunter," when she proves to be amazingly skilled at paintball, both outlining a perfect group strategy and doing several forward flips to knock away Mr. DiMartino's gun.
- She also had an earlier one in "The Misery Chick" when she slapped the "hero" quarterback (he asked her to have sex right after she said her boyfriend worships him).
Quinn proudly stating that Daria is her sister, followed by Stacy and Tiffany taking Sandi down a few pegs by stating that they both already knew and were just being polite by not calling Quinn on her numerous "cousin" statements.
- In the same episode, Daria managing to teach an English class despite no prior teaching experience, and "in the face of near-total misanthropy," and break down Romeo and Juliet for the class to the point where most of the students actually got it.
Stacy snapping on Tiffany and calling her out on being hopelessly self-absorbed in Fat Like Me. Sure, it didn't have much of an effect on Tiffany (not much does), but it was still amazing to watch.

"How come?! Because I can't take it anymore. I'm sick of doing all the work while you just sit there. I tried my best, and even if it wasn't as good as Sandi's or Quinn's, a chain is only as strong as its weakest round thingy, and you refused to lift one freakin' finger! I'm through running the Fashion Club all by myself while you (imitates Tiffany) staaaaaare... in the miiiiiiirror... and taaaaaalk... about yourseeeeeelf... and I, I, I quit!"

Another for Stacy - Life in the Past Lane, where she manages to turn the tables on Sandi.

"Oh, Sandi. You are so naïve."

Real Life example: One member of the Daria fandom had become ill and was in a nursing facility, where he didn't have any form of computer access. Two members of the fandom got together - from different parts of the country, no less - and not only got him an Internet-capable laptop, a cell phone so he could keep in contact with his fellow fans, and took a cross-country trip to get it to him and visit.
Another meta one for Wendy Hoopes in the Musical Episode "Daria!", where she managed to give great singing performances as all three of her characters.
In the episode "I Don't," at her cousin Erin's wedding, Quinn is being hit on by a lecherous old pastor. Quinn's groomsman "partner" Garret puts an end to it:

Minister: I've just been explaining to Quinn how emotions can be very confusing for young people like yourselves.
Garret: With all due respect, Father, I wonder if maybe you're not the one with the confusing emotions...

Mr. DiMartino gets two in "Is It Fall Yet?":
- After the camp bully says he wants to be a football player, Mr. D goes nuts and verbally tears him apart before he begins to have a breakdown -- but then he hears the cheers of the kids, which insipires him to teach again.
- This leads to the second one: after Mr. O'Neil's constant weak excuses for not going outside, "Uncle Anthony" PULLS A SINK OFF THE WALL AND BREAKS A WINDOW to lead the kids outside.

"I'M GOING ON A HIKE!"

When Sandi mocked Quinn for being able to answer a question after getting tutored:

Quinn: Just because you're able to answer one simple question doesn't mean you're a pedagogue.
(Sandi is left speechless and confused because she isn't quite sure what Quinn said. Quinn, rightfully, smiles)

Stacy gets one in the ending of Is It College Yet? Sandi decides to guilt trip into performing a number of chores to make up for "almost crippling her" with her birthday wish. Stacy points out that it's still not clear if her wish was the reason Sandi lost her voice, since she got better without the so-called "curse remover". Sandi passively threatens that this could jeopardize Stacy's standing in the Fashion Club. Stacy counters by deciding to take a sabbatical like Quinn did, because her standing just isn't worth her dignity.
Ted Dewitt-Clinton gets one by calling off the Fashion Club, Kevin, and Brittney from protesting the change in the yearbook structure. He does so by A: mentioning a supposed sale at Cashman's to ward off the Fashion Club, and B: settling matters with Kevin through a grip contest, and almost breaking Kevin's hand without breaking a sweat because he practices isometrics with his dad.
Jane at the end of Is It Fall Yet? After spending months trying to be polite, she finally explodes and tells Daria off for stealing her boyfriend.

Daria: "I'm confused. What are we fighting about?"
Jane: "We're fighting about you, Daria Morgnedorffer!"

Jodie gets one in Gifted when she tells off one of the stuck-up kids at Grove Hills after he is rude to her. Daria even notices that Jodie definitely enjoyed doing it.
Daria's moment in "Quinn The Brain". For context, Quinn got a B for a poem she wrote in English Class. Initially it was implied she was gonna get bullied for being a brain, but instead it makes her more popular among the school and in turn makes being a brain a popular thing. Which in turn let's the fame go to her head. Showing no signs of stopping, because of the added bonus of pissing Daria off. Daria naturally takes offense to it, believing that Quinn making a brain look popular would set a bad example for true brains like her, by turning it into a fad. Causing students and teachers to gush over her even when she's not putting in her latest works. Looking for a way out of it, she receives a miracle in the form of the Three J's asking her for help. They mention that because Quinn is super popular for being a cute brain, she barely has time for them fighting over her anymore and they want that back. So the four devise a plan. A plan Daria regrets having to resort to. Using a photo of Quinn's original look as reference, Daria strips her original outfit and don's clothing similar to Quinn. She wears make up, styles her hair and rehearses flirty lines. Then on cue the Three J's show up loudly announcing that they've come to pick up Daria, just as Daria intentionally walks past Quinn showing off her look. She stops in the hallway and counts to three, timing the exact moment Quinn panics and rushes downstairs to greet the boys. Conceding Defeat. She later downplays the B she got and intentionally dumbs herself down. It's an awesome moment for Daria for two reasons. 1. She knows her sister's insecurities well enough that all it takes is for Daria to steal her thunder, by threatening to steal the Three J's from her. and 2. After so many episodes of so many people referring to Daria as the ugly girl in various ways, she proves the audience wrong. By showing that she can be beautiful if she wants to be, but chooses not to.