Once your characters level enough, let them loose on enemy units. Laugh as they are destroyed one by one by one.
When Elincia asks for Begnion's support in her efforts to reclaim the Crimean throne, Sanaki questions Elincia's royal status and asks her for evidence that she doesn't have and denies Ike's word on it as he is not a noble. When Sanaki reveals she knew all along of Elincia's status and that she was only toying with them for her personal amusement, and the Begnion senators laugh in amusement at Sanaki's actions, Ike does not take well to this at all, and has some choice words to say to Sanaki and the Begnion senators:
Ike: What is the meaning of this? You knew Elincia was Princess Crimea? And you continued to humiliate her for your own entertainment? For some stupid game of wits and words? This is no joke! [...] Elincia's homeland is lost to her! Her family has been hunted down and killed by the monsters of Daein! And with nowhere else to turn, she endures mortal danger and terrible heartbreak to reach your door. And then you... you laugh at her?! Where is the humor in that? Where is your decency? You're horrible! You are all horrid people! You disgust me beyond words! And you owe Elincia a proper apology.
And even before that, he has this to say when Sanaki denies Ike's vouching for Elincia's claim to be the Crimean Princess because he is not a noble:
Ike: I am neither a noble nor a knight. I have no connection with the palace whatsoever. And no matter how much gold I stood to gain, I would not betray my convictions. Elincia has paid us, yes, but nothing more than the standard fee to purchase our services as her escort. Nothing more. We have come this far only because we believe Elincia to be a woman of integrity. We would not sell our swords to a liar. I don't care how high and mighty you might be. I will not stand here and let you mock the bond of trust that ties us to Elincia.
Ike: Then we will fight... and we will save our people. Make your peace with whatever the gods worship. Your end is near.
Ashera: My end...is near?
Ike: In every battle that mattered in my life, I've always been the one left standing, no matter how slim my chances. This battle means more than any of the others, because it's for the life of every person that I've ever cared about. I will win this fight.
Soon after, he proceeds to (with good goddess Yune's power) deliver the final blow and kill a god. Complete with Ass Kicking Pose.
In Path of Radiance, Marcia, whose older brother Makalov's debts, gambling, and general Scrappyness had caused her to quit her job, fight pirates, and fly all over the country to try to find him. And what does she say to him when she finally finds him and he pathetically tries to talk his way out of it? "STUFF IT, SPONGE-BRAIN!!! NO MORE LAME EXCUSES!!! FOLLOW ME!!! NOW!!!"
Marcia also has a scene where she intends to fight off an entire troop of wyvern knights by herself to protect Elincia, Leanne, and Nealuchi (a queen, princess, and princess' royal retainer respectively), and spouts a constant stream of insults at them the entire time. She even manages to yell at Haar in the midst of the battle to make him help her.
Elincia in Radiant Dawnhas the confidence to lay down her weapon in between two warring armies just to prove a point.
Sanaki's conversation with a certain subordinate near the end of the game... Doubles as a Funny Moment.
Sanaki: You are my subordinate, after all. I've decided that leaving one's empress to die is punishable by drowning in a pool of rancid butter.
Sephiran/Lehran: Of course it is, my empress.
Sanaki: I hope you're a strong swimmer.
Leanne is the cause of one when she arrives in Crimea in Part 2 of Radiant Dawn. Paraphrasing the narration: "The Crimean nobles don't like how Elincia welcomes the Heron Princess to court so readily, but they know that if they say anything Tibarn and Naesala will tear them apart, so they shut up about it."
The end of Part 2, involving the Greil Mercenaries' Big Damn Heroes return to rescue Lucia from execution.
Kurthnaga's Big Damn Heroes moment at the end of 3-13, levelling a castle with a single attack to provoke a ceasefire.
Vantage combined with Wrath and Resolve. Basically, if a character has all of these skills and ends up in a really bad situation, they turn into a One-Man Army.
Whenever a heron manages to get a kill in Radiant Dawn with a magic card.
Soren gets a few:
Repeatedly mouthing off at the battle-thirsty lion laguz general and future king of the beast tribe Skrimir, knowing that the latter respects him and can't win the war without him.
If he fights Micaiah during Part 3, chapter 7, he outright insults her. Note that, while Micaiah is not evil, everyone treats her with much more sympathy than her concrete actions elicit, and he Meteors her. In the face. Usually twice. Best yet, performing this Moment of Awesome is one of the steps to unlocking a secret ending scene.
Soren: "Do not presume to understand me, you ridiculous girl."
Soren essentially makes all the strategic decisions in relation to Ike's army, which means he has a direct hand in bringing down Ashnard, his own father.
The sequence as a whole is a Moment of Awesome for Lucia. The poor battered-looking young woman remains defiant to the end as she declares her loyalty to Elincia moments before she is to be hanged. Lucia's response to Elincia's decision to sacrifice her for the good of the country? "Hah!"
Similarly, the scene beforehand is a Moment of Awesomefor Elinciaas a queen, because she made the hard choice to let her beloved friend Lucia die not knowing all of this was about to happen.
Haar: Why couldn't you just stay on patrol? Saw a pretty little heron and just had to have her, is that it? I could never decide if you were more greedy or more corrupt. Stupid was never in the question, though. Zeffren: Who do you think you are?! You're a traitor, just like Shiharam! The dracoknights spit on your name! Haar: ... Do they now? Well, here's your chance to try the real thing.
How about the fact that once he becomes a dragonlord (which can happen on the last part of the second chapter), he ends up nigh on invincible. topped off with about a 30% chance of unleashing stun (3X damage and paralysis), plus huge strength, defence and killer axe, he kills all in seconds... whilst half-asleep.
Haar is so awesome that when he re-recruits Jill in the midst of a heated battle where they are on opposite sides, she's swooning near the end of his speech.
Haar's conversation with Levail in the Tower of Guidance gives Moments of Awesome for both of them.
Levail: He is the last true knight. I will die for him. Haar: Yes, Levail. You will. Levail: How I dreamed of fighting a proper foe! I am honoured, Sir Haar! Have at you!
Tauroneo's exchange with the Mad King Ashnard is a brilliant and particularly poignant illustration of the man's character and is severely reminiscent of General Duessel, the Obsidian, from The Sacred Stones.
Ashnard: Is that you, Tauroneo? As I thought... You betrayed me after all. Tauroneo: ... Ashnard: In my father's time, there was a man who was one of the Four Steadfast Riders. That man grew old and useless, and retired from the front lines. How does his story end, you ask? Come, let us write it together. Tauroneo: Oh, my king... In all of Daein's history, perhaps no other ruler has used the talents at his command to the degree you have... But all the same, no other king has chosen a path so incredibly stupid. Ashnard: Heh heh heh... Will history judge me to be just or evil? We will not know until all of this is finished. Tauroneo: ...Now that I've confronted you and traded words with you, I have come to a decision. Throughout Daein, I, Tauroneo, will be known as the king killer. Come! Let me earn my name!
When Lucia and Bastian have resigned to leaving Geoffrey behind as a decoy, Elincia refuses to stand for it. Lucia orders Ike to lead Elincia to safety, and he adamantly refuses. His reasoning? He still has a contract with Elincia personally as a mercenary, and is thus insistent upon doing the mission to save Geoffrey that even Geoffrey himself and his own sister believe is not worth it. The fact that Elincia and Geoffrey can get married in the sequel makes it well worth his trouble.
Sothe getting promoted to Whisper by Yune. He seriously says he feels great — so great he could arm wrestle with Skrimir.
Most of the boss dialogues in Part 4, especially against Izuka.
Bastian: Exactly, yet you had no hesitation before doing worse to the laguz. I will speed you now to the afterlife, where you may contemplate your life's egregious mistakes.
Volke simply gets to the point.
Izuka: You! You're...
Volke: ...Under a new contract. Good-bye, Izuka.
They also save plenty of choice words against Lekain.
Sanaki: Burn, traitor!
Elincia's amazing Rousing Speech before the assault on Ashnard's palace is both this and a Heartwarming Moment. Especially when you consider how quiet she was throughout the entire game. Even Ranulf was impressed!
If you decide this way, Ike can give one as well. It's shorter, but just as awesome.