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? The inevitable result of the call is 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.
Jake: You see, Helen, if this was supposed to be macaroni and cheese, it would be very bad. But it's penne a la pesto, and judged by the standards of penne a la pesto, it's very good. Helen: Jake, what the hell are you talking about? Are you listening? Jake: Of course, sure. What I mean is, if this poster is supposed to be propaganda promoting student life, it would be very bad. But if it's supposed to be art expressing Daria's personal vision of student life, it's very good. See? Daria: (surprised) Thanks, Dad!
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.
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). Although, what really provoked her was when, after Brittney repeated that Kevin is Tommy Sherman's biggest fan, Tommy completely missed her point and asked "What are you saying? He wants to watch? I don't know..." and then she slapped 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.
What makes it even better is that, when they said they were "just being polite," it might not have been referring to Quinn...they may have gone along with it to avoid SANDY being embarrassed by being the last person to realize the truth.
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 na´ve."
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.
When Sandi mocked Quinn for being able to answer a question after getting tutored:
Quinn: Anyone can answer a simple question Sandi, it doesn't mean you're a pedagogue.
Sandi is left speechless and confused because she isn't quite sure what Quinn said. Quinn, quite rightfully, smiles.
Stacy gets one in the ending of Is It College Yet? Sandi decides to guilt trip her 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 mentioning a supposed sale at Cashman's to ward off the Fashion Club and settling matters with Kevin through a grip contest (where he almost breaks 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 gets two in Jake of Hearts:
Shaming Bing and the Spatula Man, the two moronic radio DJs who've been broadcating from the school and pestering Daria all week, into leaving by saying on air how she's been dealing with Jake's heart attack the entire time and those two have been making it worse. The two don't even say anything when Daria finishes her short monologue. They just pack up and drive off.
Pointing out her grandmother Ruth's hypocrisy when she, once again, tries to get Helen and Quinn to conform to her idea of a comfortable lifestyle even though she admitted to Jake that she wished she could've lived her life differently then she had while married to Jake's asshole father.
Daria (to Quinn and Helen): You both owe me.
Helen: How does she do that?
Quinn: You got me.
Daria and Quinn dismantling the feud between Helen, Rita, and Amy by mimicking their petty arguing.
Daria: Gee Rita, are you ever gonna get a real job? Why should I Helen, when you won't pay attention to mother. And you Amy, who asked you?
Quinn: Yeah, you had a dance floor at your wedding!
Daria: You're a show off and a know-it-all!
Quinn: You just hide in your room like a kermit!
Daria: Mom likes you better!
Quinn: That's because I call her better!
When Quinn aces a writing assignment at school (to the surprise of everyone and herself), the success goes to her head and she turns into a poser beatnik. When Quinn begins to horn in on Daria's territory, Daria gets her to back off by dressing up like Quinn and having her three male 'followers' show up at the house to ask her out on a date. The end result: Quinn freaks out, goes back to her old self, and says she stole the essay from somewhere.
Quinn's successful essay counts as an in-universe Awesome Moment for her — and foreshadows her Hidden Depths character arc in the final season/finalÚ movie.