Sometimes dispassion is the best motivator.
In fiction, like enthusiasm, the lack of enthusiasm can be harnessed as a weapon. It takes more than just turning around and trying to pretend your problems don't exist. You have to mean it. Feel your lack of investment in the conflicts around you and declare to yourself and the world "I DON'T GIVE A RAT'S ASS!"
The Power of Apathy is usually done under cynicism. Just as the form of media the trope manifests in is meant to represent an absurd deconstruction of the monomyth or the genre that it inhabits, The Power of Apathy is meant to be a twisted parody of The Power of Love, The Power of Hate, The Power of Friendship and whatever power you can get out of all of the other emotions.
Common applications of The Power of Apathy are usually done in circumstances too immense for a character to realistically overcome. Perhaps the protagonist is facing against The Horde spanning infinite legions, or a giant, indestructible Kaiju parent who just won't let me hang out with my cool new friends cause he is, like, a total b-word! What is the solution? Just Ignore It. And not just ignore it; get on with your life and find something better to do. The armies and the monsters will get frustrated getting your attention and either go home disappointed, or the apathy with physically hurt them as a Literal Metaphor. Because of this, The Power of Apathy is a power usually Played for Laughs. The times it is not is usually to counter those empowered by Clap Your Hands If You Believe. Compare Sheathe Your Sword, which involves winning by deliberate inaction rather than apathy per se, and Safety in Indifference for characters who are deliberately (and usually unsuccessfully) trying to invoke the trope.
- In Uninvited Guests, Hitsugaya eventually snaps and takes on a very Zen-like perspective. One of the things this perspective teaches him is that he can rely on the plot to solve all his problems eventually. Since he has no internal conflicts to entertain potential readers with, the plot consequently resolves itself much faster and smoother.
- The evil wizard Ommadon from The Flight of Dragons tries to frighten and cow The Hero by expanding himself to giant size, with multiple hydra-like heads. The Hero, however, is a man of science, who refuses to believe in Ommadon's magics. Instead, The Hero cites principles of physics and biology that refute Ommadon's powers. By remaining The Stoic throughout the contest, The Hero sees the Villain expend himself entirely in fruitless bluster and theatrics.
- Pitch Black from Rise of the Guardians finds that the town's children refuse to be cowering and fearful of his powers, those powers diminish to the point where he becomes the most afraid. The children's combined disbelief reduces Pitch to insubstantial and ineffectual, his worst scenario. As a result, his nightmare mooks, who can smell fear, turn on him.
- Aliens Steve Perry Trilogy: Wilks has this. Near the end of Nightmare Asylum, he recalls a psychiatrist telling him about Doc Holliday, and how he survived against deadlier gunslingers despite subpar skills because, with his tuberculosis diagnosis, he honestly didn't care if he lived or died in any given moment. Wilks embraces "Doc Holliday Syndrome," believing he's been living on borrowed time ever since Rim. Nothing the Aliens can do to him frightens him, since it should have happened to him a decade ago, just like the rest of his platoon. And if he's beyond caring what the Xenomorphs can do to him, he certainly has zero fucks to give about anything a human being could threaten him with, no matter how much rank, status, money, or power they can claim.
- Warhammer 40,000: The planet Aphexis is populated by people who simply do not care- Chaos forces have repeatedly conquered the place only to find that the inhabitants don't give a rat's ass about the vast displays of cruelty their captors put them through.
- At the end of the Warrior #4 Linkara/Spoony Crossover review, Spoon and Linkara realize that the time and effort they took bashing the titular comic is what was causing the multiverse to collapse, and that they must stop caring about it in order to prevent the apocalypse. They reach out to the audience and plead with them to announce that "these comics suck and I don't even care anymore." The spacial rift diminishes and the multiverse is saved, but Spoony, Linkara and Insano end up turning into Grey Lanterns, the Guardians of Not Giving a Crap, complete with everything becoming black and white. This soon goes away when Insano asks if they want to watch TNA Impact.
- In the Ninja the Mission Force episode "Bruce - A Dragon Story", the knights manage to defeat the Troll by ignoring it, the troll crying out "pay attention to me" as it dies from lack of attention. Later, the hero of the episode manages to defeat Number 34 through apathy, even proclaiming "I don't care" as he stabs it.
- Lumpy Space Prince in the Adventure Time episode "The Prince Who Wanted Everything" defeats his monster parents through the power of apathy, screaming "I DON'T CARE" at them through a microphone, reducing them to a lifeless pile of lumps.
- In the Futurama episode "I Second that Emotion", Bender is implanted with an empathy chip tuned to Leela's emotions. When Bender has to save Nibbler from a monster, he can't because Leela is too emotionally distraught. So Bender has to teach her to not care about Nibbler... for the sake of saving Nibbler.
Bender: Listen to me, Leela. I'm an expert at not caring. The secret is to stop giving a rat's ass about anyone else and start thinking of the things that you want, that you deserve, that the world owes you.
Leela: Well, I could use a new tank top.
Bender: Bigger! Bigger!
Leela: A fashionable tank top, and fashionable boots... encrusted with jewels.
Bender: Don't stop now! You need pants to go with that outfit!
Leela: Yeah! And I could afford it all if I didn't have to feed that stupid Nibbler!
Bender: Bender is back! I'll save you, Nibbler!
- One episode of Wander over Yonder has the Main Characters confront a monster called the Troll, who feeds off of negativity. He constantly insults and taunts Prince Cashmere's goat army, and he gets bigger and stronger every time he gets a rise out of them. How do the heroes defeat him? By ignoring him. Once they stop reacting to the Troll's jeers, the Troll loses his power and shrinks into nothing.
- In the The Simpsons episode "Attack of the 50-Foot Eyesores" segment from "Treehouse of Horror VI", giant billboard mascots come to life and rampage through Springfield, and the only way to make them inanimate again is by not paying any attention to them.