Look at the main page quote. Reflect on this simple fact: Captain America looks up to Daredevil. Steve Rogers, the Star Spangled Man With A Plan, the Marvel Universe's Big Good, looks up to Matt Murdock. That should tell you exactly how awesome he is.
In the "Man Without Fear" miniseries by Frank Miller, Matt deflects not one, but two gunshots with a stick, and one of them was struck back at the shooter. With. A. Stick.
Born Again, what does Daredevil do when his girlfriend turns into a drug-addicted porn actress, who tells Daredevil's secret identity to the guy's worst enemy, enemy who uses all of his influence and conections to make sure Matt's life becomes a living hell? He. Fights. On. That's what.
A comparatively minor example can be seen in the A VS X miniseries, depicting Daredevil fighting Psylocke during the war between the Avengers and the X-Men; at one point, Psylocke tries to read Daredevil's mind and is literally overwhelmed by the sensory input she receives in the process. Consider that; Psylocke, a trained psychic and warrior ninja, couldn't take a few seconds of processing what Matt Murdock has to deal with every single moment of his life. It's hard not to admire someone capable of something like that.
Every fight with Bullseye:
At the end of the Elektra Arc when Matt breaks Bullseye's back
Shortly after getting married, when he scars the cross-hair into the psycho's forehead
During the Murdock Papers arc, when he threw him in front of a bus
Shadowland #1, when Bullseye makes the ultimate Oh crap face.
At the end of the Hardcore storyline, when he beats the holy crap out of the Kingpin, throws him through a bar's window and proceeds to tell the next speech to every crook in attendance:
Daredevil: This is the Kingpin! Your Kingpin! This is Wilson Fisk! And I beat him with my bare hands! And this man is going to rot in jail for the rest of his life for the hell he has made of this city! And if I could do this to him, imagine what I could do to you, any of you! If, from this second forward, you sell your drugs! Rob! Or whore! Anywhere near my city - if you can't control yourselves, if you can't figure a way to be productive in this life... Find somewhere else! Far from here! Far, far from here! I am here to say: if you people so badly need some sort of Kingpin, someone to lord over you - Well, from now on... it's me! I am not protecting this city anymore. I am running it! And I say: the people of Hell's Kitchen are my people. This is my territory now -And I say GET OUT OR CHANGE! Tonight! You think you know me? You think you know who I am? These are the new rules. This is how it will be from now on. Spread the word. And if you think I'm kidding... Look at the carcass in front of you— LOOK AT HIM!
Earlier in that same issue, Matt gives Kingpin a final warning before commencing the beatdown.
Matt: No, Wilson. No. This is it. Right here. This is the end of the road for us. You're done.
Kingpin: You should know me well enough by now to know - its done when I say its done.
Matt: No, its done. Im sick of outwitting you. No more games. No more chessboard of life. Now Im think Im just going to beat the $%#@ out of you!! [proceeds to beat seven shades of crap out of him].
That one time when he detected a sniper in the next rooftop by feeling the laser of the rifle's laser scope against his skin.
During the non-canon oneshot Punisher Kills The Marvel Universe, The Punisher has, as You may have guessed, killed every hero and villain in the MU, including Hulk, Spider-man, Iron Man, X-Men and others. Frank kills some of the most powerful and most intelligent people in all of comics but Matt manages to survive right to the end and even tries to still reason with Frank. It pretty much cements his status as "The Man Without Fear" that he is able to calmly speak to a man who has murdered Godlike heroes and villains without panicking. In fact, Matt nearly stopped him and only died because he tried to reason. That is truly Badass.
His return in Daredevil: Reborn.
Matt Murdock: I have faced my fears and came out the other side!! I AM NOT AFRAID!!
During the Acts Of Vengeance crossover, where Loki had a legion of supervillains do an Opponent Switch, Daredevil ended up having to deal with Ultron, who can take on teams of Avengers singlehanded and is far out of Matt's weight class. Even worse, it's a completely mad model who's building himself a mountain throne of other Ultron heads in the middle of Central Park. Matt realized that Ultron's adamantium skin may be invulnerable but his joints are simple steel - so he beats a raving Ultron's head off with a stick.
The moment in Hardcore when he is pushed over the edge by Bullseye's attempt to murder Milla and proceeds to beat about the everloving shit out of him whilst delivering the mother of all "The Reason You Suck" Speech's to him, telling him that he is a worthless waste of space and will die unmourned. Then he carves a bullseye into his head and lets the police take him in. If ever there was a reason not to piss off Matt Murdock, this was it.
Daredevil: I went looking for you, Lester. Did you know that? While back—I decided I was going to find you and kill you in your sleep. I was going to kill you and no one would ever know I did it. And in looking for you, I finally found out all about the big mystery that is you. Your secret, secret origin. And I know why it's a secret. It's pathetic!! I know about your prostitute of a mommy and how you don't even know who your daddy is—I know what happened to you in high school—I know!! And after finding out your entire pathetic, uninteresting story—I know why—I know why you keep coming around here, Lester!! You keep coming around here because you want me to put you out of your misery! Because you don't have the guts to do it yourself!! But I'm not going to do it!! You hear me?!! I'm not getting sucked into your nightmare!! Because I just don't care!! You here me, Lester, I don't care about you!! No one cares! You're an animal! Your mommy doesn't care. Your daddy never cared!!! No one cares if you live or die!! You mean nothing!! You are nothing! What is this? Huh? What is this, a tattoo on your head? You psycho!! What is this supposed to be? Your logo? Your super cool bad ass logo?
Bullseye: It's your—
Daredevil: Shut up, animal!!! You want my attention—I'll give you my attention. I'll give you some meaning. I'LL GIVE YOU SOMETHING TO THINK ABOUT!! THIS CIRCLE...IS FOR ELEKTRA!!! And this circle...is for Karen!!! And this center point right here...is for when you finally realize that no one cares!! That I don't care about you!! That Kingpin USED you!! That you serve no purpose in this world!! That you mean NOTHING!! And when you FINALLY realize how pathetic and disgusting you REALLY are...And you FINALLY have the GUTS to do what you are begging ME to do FOR you—WHEN YOU FINALLY HAVE THE GUTS TO END YOUR MISERABLE EXISTENCE...!! HERE!! AIM TRUE. Aim to kill.
The Absorbing Man is a guy who can absorb the physical properties of anything he touches. Daredevil is a badass whose powerset consists of heightened senses and a personal radar. You'd think it'd be a Curb-Stomp Battle, right? Wrong - when the Absorbing Man goes on a rampage in downtown Manhattan, Daredevil takes him on and takes a serious beating, but then we see why Matt Murdock's been able to triumph over villains who completely outclass him in power. The Absorbing Man absorbs the properties of the diamonds he's stolen, and suddenly becomes as hard and strong as diamond. This gives a badly wounded Daredevil the opportunity he needs, as he uses his radar sense to find all the little flaws that appear in the Absorbing Man's diamond body and start chipping away at them. Eventually, the Absorbing Man literally falls to pieces from all of Daredevil's attacks, even though DD is just about ready to collapse. Keep in mind that the Absorbing Man is a regular dance partner of both The Mighty Thor and Incredible Hulk.
Matt's ruining of Kingpin's plan to escape from The Raft. Following Fisk's plan would require letting Fisk go and relying on Bullseye's help. So Matt, with the assistance of the warden, who he had befriended, and the Punisher, who had snapped him back to his senses, he leaves Bullseye and Fisk injured and makes it out, while simultaneously making himself appear to be Castle's hostage, which works towards clearing his name.
While they were both in the prison, there was a combined CMOA for both Fisk and Matt. When a rival mob leader put a hit on Foggy Nelson and framed Kingpin for it, Matt, armed with a hidden knife, went for Fisk. Fisk calmly explained all the reasons why he wouldn't do it and the reason why he has no need to do it, and then calmly states to Matt that if he doesn't believe him he can stab him with the hidden knife, which Fisk had spotted. Matt and Fisk then team up to unleash a can of whupass on the rival mob
Vanessa Fisk's plan to get back at Matt and Wilson. She offers to fix Matt's Secret Identity problem under condition that Matt get Wilson out of prison. He turns her down. She does it anyway. This makes Matt feel morally obligated to uphold his end of the deal, and Fisk gets out of prison. As last acts go, it's pretty up there...
Also, Matt spins it pretty well. He makes Wilson give up his American citizenship and tells him to live a good life for Vanessa.
Daredevil confronts Ikari, a new villain with his same power-set. At first, DD thinks it'll be an easy fight, since he's had his powers far longer than Ikari. However, as the issue goes on, DD begins to doubt this. They are evenly matched, battered, and exhausted, DD moves the fight to an abandoned sporting goods store. DD hides and turns on the fire sprinklers, which dulls their senses. DD moves to grab a baseball-bat, thinking that Ikari has no way to know he's right behind him. Until Ikari turns around, looks at him and says "Try the red one." DD makes the sudden realization Ikari isn't blind, just before Ikari beats him within an inch of his life, telling him the only reason he didn't kill him is that his master wants DD to be afraid first.
Foggy Nelson in the 2012 series. DD has just received the thrashing of his life from Ikari. Meanwhile, Foggy is in the hospital, having been diagnosed with Ewing's sarcoma. DD rushes to his side and rescues him from being killed by the still-unknown Big Bad. Foggy insists that his BFF has to calm down. By now, Matt is totally frazzled, facing an enemy who has all his heightened senses plus sight. And he doesn't know who's pulling Ikari's strings either. So Foggy takes the lead and helps DD figure out the identity of whoever's behind all these attempts to kill him. Surpriiiiiise! It's Bullseye. Foggy does all this while battling cancer. Which is...actually kinda badass.
After a confrontation with Bullseye, Bullseye is left blinded, essentially a prisoner in a flesh and bone coffin — his mind works, but he's paralysed and blind. Foggy asks Matt if he tried to save Bullseye's sight, and his response is made even better because it isn't a boast; it's a simple statement.
Matt: I did what was right.
Foggy: Of course you did.
Daredevil is essentially holding Bullseye hostage as Ikari comes at him. However, Bullseye says he has agents targeting Matt's loved ones, and we see people watching Matt's employees, Foggy, Kirsten and Milla. Bullseye says that, if Matt doesn't battle Ikari to the death and lose, those people will die... Que the reveal that Matt actually had his superhero friends watch over those same people. Doubles as a Heartwarming Moment.
Daredevil's Batman Gambit against Mister Hyde and Cobra. After Mister Hyde uses his scientific skill to create a chemical which took away Daredevil super senses, leaving him totally blind, he fools them into thinking he has regained them by doing some crazy acrobatics in front of them the next day, making them rush to Hyde's laboratory to make a stronger dose. Daredevil follows them and then snatches the antidote right out of Hyde's hands and repowers himself, then tricks them into fighting each other. While they are fighting, he tricks them into a trap and finally hands them over to the authorities. Checkmate.
Bonus points for fighting Thor and convincing him that he can hold his own against Cobra and Hyde
In a recent issue of Charles Soule's run of Daredevil Matt decides to put a hit out on himself as a way of taking down more supervillains and help pay for his partner; Blind Spot, medical bills who had his eyes gouged out by the serial killer muse.
In the next issue Bullseye attempts to shoot Matt with a high power sniper rifle. As the Matt's inner dialogue reveals he is tempted to let Bullseye kill him after having lost faith in thinking that everything he has done in his years as a hero have made the world a better place. It isn't until he remembers what a priest who he had been consulting earlier on his break in faith had told them that God gave humanity an imperfect world and gave humans the ability to see that is imperfect and to make it better as a way of making sure once the goal of a perfect world is achieved that we will never let it go. Forward to the present Daredevil BLOCKS it with his club. As Matt proceeds to beat the living crap out of Bullseye again we get this beautiful monologue that sums of Matts heroism and selflessness wonderfully:
Matt: I will never see a perfect world I'm blind to it. Its Darkness for me everywhere. Deep, endless. I'm not fighting for myself I'm fighting for everyone— so they might get to see it. I will fight. Forever. For Everyone whether they know it or not. Whether they are watching or not.
The 5 part Man Without Fear miniseries. After having barely survived being hit by a truck Matt is over the course of the series afraid to become a superhero and even says to countless friends and allies that hes quitting and while he tries to recover he is tainted by a psychological emodiement of Fear. However after scaring off Kingpin (who had come to kill him while he was in the hospital) Matt comes to terms that while he is afraid hell be damned if hes gonna let that stop him from protecting his city.
Dardevil: I am Daredevil. And I am afraid. But Ill die before I let them have my city.
Bullseye is very much this. His demand when he's told to kill Elektra and Daredevil?
Bullseye: I want a fucking costume.
Plus when he kills Elektra... It's so hammy.
Bullseye: You're good, baby. But me... I'm magic.
(Bullseye flicks out an Ace of Spades and slices Electra's throat with it. Then he catches her thrown sai and grabs her.)
Bullseye: And for my next trick...
(He stabs her, making the sai 'disappear'.)
Young Matt effortlessly humiliating the trio of bullies who were getting their kicks by picking on a blind kid.
To elaborate, before Matt's accident, they beat him up after goading him into a fight. After Matt's left blind, they find him in the same alleyway & mock him for his accident, before challenging him to fight. As they start to walk away, Matt calmly responds "okay" and proceeds to repeatedly slap the lead bully across the face with his cane, before tripping him up after he throws a punch. A second kid runs at Matt, only for him to move & send the kid running into the garbage, and then Matt promptly knocks the final kid on his ass with a backflip kick.
The dialogue at the end pretty much tells us viewers of the end of Kingpin's Career.
Kingpin: You hear that blind man? They're sirens, they're coming for you
Dardevil: For me? Didn't you hear? The word's out on the Kingpin, they're coming for you. I can hear the police radios from here.
Kingpin: No...I swear I'll tell them who you are.
Daredevil: Go ahead, tell them. Tell the guys at Riker's all about how you got beat by a blind man. It'll be like blood in the water.
Kingpin: Don't you worry about that, because I'll get out.
Daredevil: I know, and I'll be waiting. Justice is served.
Before that, we see Daredevil gain the upperhand with his Radar sense and finishing it off with him breaking both of Fisk's Kneecaps in one swift motion. You could hear the bones crunch twice from it, once from the kick and the other from Kingpin falling onto the ground, causing him to scream in immense pain. In the comics, Daredevil crippled the Kingpin. In the movie, he made him scream when he did it.
The bar fight scene where we first see Daredevil in action, it's even more awesome in the director's cut.