The time Yuki went berserk after his father was killed and managed to take out most of Eleventh's men by himself, with Yuno only coming in to finish off the last one.
Yukiteru's entrance into the Hall of Causality (pictured above) after his Heroic BSOD is all kinds of Badass. He then proceeds to tell the other players how he deduced the Eleventh's identity using his diary and declares that he will be the one who will win the game and become God. It's a bit mitigated by the fact that Yuno scripted their confrontation, but damned if that wasn't the moment Yukkiteru finally got his shit together.
After dropping out of the spotlight for a few chapters, Yukki makes his re-entrance by saving Minene from 11th's henchmen with a machine-gun.
How Yukki found out the vault combination was pretty damn good too.
Yuno has a lot of these moments throughout the manga. One of the most celebrated/hated in Chapter 50/Episode 22, during the battle between Yuno and Akise, Akise seemingly destroyed Yuno's diary. However, it's not long before we realize that Yuno is still kicking when she whips out her real diary while slashing opening Akise's chest. In other words, Akise was actually outsmarted by Yuno and got owned by her at the same goddamned time.
The events leading up to that moment were pretty damn badass too. Yuno outsmarted Akise every step of the way, first by turning his own diary against him. His diary stated that he would take down Yuno (though he had no intention of killing her) and once he pinned her down, she stabbed herself. The reason? She knew that Yuki would be furious if Akise murdered her, and she knew that Akise wouldn't want to lose Yuki's affection. This forced his hand and made him release her and bandage her up. It also changed the future in her favor.
Afterwards he ran off to call Yuki and tried to call him to warn him, but Yuno was already a step ahead and had called Yuki first. And she used both Yuki and her own diary masterfully, knowing full well that Yuki couldn't see what would happen to him and that his diary mentioned that she had been stabbed, but not the details of the stabbing. And then comes her manipulation of Yuki that leads him into killing Hinata. Yuno is fatally bleeding as she works this manipulation. And then she almost dies laughing at it's success. It's a truly Magnificent Bitch moment for her.
She also thwarts his last effort to get a message across to Yuki. It seems any awesomeness done by Akise is responded to with more awesome from Yuno.
The way she determined which Twelfth was the real one.
In Mosaic Chapter 4/Episode 10 with the reveal that his armor is not only bulletproof but bombproof as well.
In the 3rd-world, pulling a gun on Yuno, who already became a god in an Alternate Timeline.
Turning Yukiteru's own house into a a gas filled deathtrap right under his own nose counts.
Manipulating the First, Second, and Fourth by using the captured Ninth as bait.
Marco & Ai (7th):
Their introduction has them mowing down the security that Akise set up, when Yukiteru thinks they're cornered due to having their apprentice diaries disabled due to the signal cut-off from the cell tower, They just simply throw those diaries away and whip out their real diaries.
Marco delivering one of the most awesome verbal beatdowns to the main characters pointing out the flaws in their relationship at a collapsing tower, with a pipe in his gut to boot.
Bestowing Kosaka the power of prediction via apprentice diary which helped save his and his friends lives.
Keeping her diary secure from the police in her person.
You have to admit, her making third place in the Survival Game was extremely badass, considering she and her orphans never killed any diary owners themselves.
Threatening to kill Deus upon being made a participant.
Her fight with Nishijima against the Third. Forced to a corner, handcuffed to a cop and down to one last flash grenade, luring Hiyama into the Music Room, detonating the flashbang with sound amplification thus defeating Hiyama.
With her eye pierced and the Fourth saving that she has nowhere to run, she responds by breaking out smokescreen and escapes on a motorcycle.
Rescuing Yuki and Yuno from the Fifth's deathtrap, giving them the antidote to the poison and giving a warning to Yuki about Yuno.
Getting Nishijima to arrest the Fourth, by telling him that Fourth is the one behind the murder of Tenth, which Yuki and Yuno were framed for doing. The anime even added that she had recorded her deal with him to solidify his guilt. Upon his arrest his diary no longer works and is forced to commit suicide.
Appearing before Yuki, Yuno, John, and Kamado in a motorcyle with Akise in tow who has dirt to deliver on Yuno.
The best part is that she pulls a grenade so that all of them can listen.
Her raid of the Eleventh's base where she, Nishijima and three teenagers all exploit the weakness of his diary, by overwriting their entries confusing him. He gets a way around it though.
The above was only possible because she asked Deus how the Eleventh's diary worked and he complies, but not before piercing her with his arm.
Her blase reaction to her right arm being blown off. She actually showed more reaction to Nishijima getting shot.
She isn't even hampered one bit despite her right arm is now a bloody stump.
Later she hits Yukiteru with it. So hard that her eyepatch goes flying.
ALL WITHOUT FLINCHING!
Arm blown off, shot in the gut. Losing a LOT of blood in both situations. Still manages to stay standing. Shocking both Yukiteru and the Eleventh. She resolves to use her final weapon against the Eleventh.
In the 3rd-world he proves his worth by successfully capturing and restraining Takao Hiyama.
Akise's decision to Screw Destiny and go save Yukiteru by creating his own diary. Right in Deus's face.
A chapter or two later, he is stabbed and slashed in the neck by Yuno. Knowing that he's pretty much screwed, he decides the most he can do is give Yukiteru a final warning about Yuno by texting it into his cell, running up a hill, and shoving the message in his face. And so he does. AFTER BEING DECAPITATED. What a Determinator...
Not to mention how out of every character in the series he managed to be the one who pissed Yuno off the most with the simple act of kissing Yuki in front of her. Why did he do it? He wanted to show Yuno that he could. He knew how Yuno would react but he still did it anyway before facing her in a fight. Though Yuno ends up getting the last laugh here (see her own awesome moment), anyone who is brave enough to make her mad on purpose should be called a badass.
While most of Kosaka's "Shining Moments" fall rather short, he does get his moments such as his rescuing Yuki when he was tied up as a hostage to Yuno.