Any time a particularly well-timed Dual Strike or Support Block occurs can make you want to cheer.
Better yet, if you're lucky enough when facing a particularly tough enemy, you may be able to see a Dual Strike with two critical hits. Pairing up a Dual Strike with two of the better crit quotes makes it even more awesome.
Or if speed allows for two strikes from the attacking unit...and then the supporting one Dual Strikes twice. Almost makes you feel bad for the other guy.
Once the villains get big enough to have their own crit and Mastery skill quotes, you can get excellent exchanges. Nothing counters Validar's "this was all written" quite like Chrom's "anything can change."
Once characters start unlocking their Mastery Skills, max out their stats, and Pair Up with someone they have a high support with (especially if they're married), just about any single battle has a good chance of becoming this.
The icing on the cake is Grima's reaction. Seeing this incredibly cruel and evil demon once so smug in his invincibility and incredible power begin to visibly panic in fear of knowing he's going to die for real is very satisfying.
Bonus points if Avatar scores a critical when fighting Grima. "Checkmate!" is of course the best one, since it could be the blow that wins the whole game for you, but even simple lines like "Here's how it's done!" suddenly take on new meaning against the Avatar's Evil Counterpart.
"Finished!" is also incredibly fitting for the situation.
Scoring a critical with either Chrom or Lucina. "Anything can change!" and "Hope will never die!" are spot-on for the moment.
Even better, after recruiting them through the Bonus Box, the player can deploy every SINGLE lord from the previous games to fight alongside Chrom. While none of them speak, it feels pretty damn awesome to fight the embodiment of evil alongside characters like Sigurd, Lyn and Ike.
Sadly offscreen, Lon'qu defending Lissa from a random band of assassins (including archers) single handedly during their A support, which is an impressive feat even when you're controlling him in battle.
There's a surprising number of "action-y" supports in this game, such as:
Female Avatar and Aversa escaping from a group of assassins by working together, in one of their supports.
Sumia refuses to let go of the beehive she found for herself and Gaius even when the bees have stung her all over, because she wants to help Gaius to get honey that badly. Gaius is extremely impressed by her pluck.
The Plan of the Avatar as revealed in Chapter 23 is incredibly awesome.
The Avatar then proceeds to blast Validar with Thoron, shutting him up.
The Avatar's rather philosophical speech in Chapter 14, in which he tells Chrom that people aren't controlled by fate, but instead walk their own paths in life, strengthened by the invisible ties between them and others. Particularly good if you're playing a Male Avatar and have already achieved an A Rank Support with Chrom, as it comes across as something of a Meaningful Echo of the speech Chrom gave to the Avatar in that support.
Morgan also says something similar to his/her non-Avatar parent, suggesting that the Avatar still believed in those words even in the future. Though which future is up for debate, given Morgan's unknown origins.
And then there's Emmeryn, who put the badass back in Badass Pacifist. Her back story alone is incredible. Not only did she ascend to the throne at the age of nine, but she undid her father's ugly legacy of religious genocide and turned Ylisse into the most beloved and peaceful nation on the continent. Let alone that in-game, she's absolutely fearless. Going back to a war-torn nation where her capture is nigh-inevitable, because she won't abandon the people she worked so hard to protect? Sacrificing herself to stop the entire ruling bloodline of her nation from being captured or killed? Emmeryn will do all that and more, and not even flinch.
Furthermore, consider that in Paralogue 20, girls from the village she's been staying at have been abducted. Emmeryn is one of them, but manages to escape. And this is after stepping off the cliff and sustaining brain damage.
The Future Past 3 gives the possessed Avatar one. S/he continues to fight from the inside to prevent Grima from slaughtering Lucina and her friends, even after Grima insists that his/her spirit has been completely consumed.
Also from The Future Past, Owain resolves to stand alone and fight the risen to allow the others to escape... Except for the fact that none of them actually left him alone
Sumia's rescue of Chrom. She may have a terrible self-image of herself, but no clumsy fool could smoothly rescue their liege from a rain of javelins! That definitely put the Badass in Submissive Badass.
"Better hold on tight, Captain... You'll be fine!"
At the start of the final battle, the entire party is knocked down to nearly no health by Grima right before it promptly absorbs the Avatar and nearly kills him/her. All seems lost, but Chrom and every character participating in the battle call out to the Avatar, and their voices reach him/her. S/he then finds the strength to break free and return to the battle, at which point Naga restore their health and they battle their way to Grima's version of the Avatar, who has a battle rating of over two-hundred! BUT can still be heavily damaged with Chrom's Exalted Falchion. Should you choose to let the Avatar deal the final blow, not only will Grima be defeated permanently, something that not even Naga is capable of, but the Avatar's bonds with his/her friends will prove to be stronger than his/her connection to Grima, and Chrom and Lissa will find their friend not too much later, only lacking the Mark of Grima.
Noire's introduction is downright fabulous. She begins in captivity by slave traders and stripped of her weapons, but as soon as she finds a bow & arrow, she undergoes a Split Personality Takeover and starts mowing down her captors like a crazy mofo!
Even better is how there are several flying units on the map, so Noire not only gets to attack her captors, she gets to hit many of them For Massive Damage. Too bad for them they had to imprison an archer, huh?
Tiki's recruitment Paralogue is this, since it's one of the few missions in the game where the enemy can easily back you into a corner even on Normal due to the fact that it is an Escort Mission, where you have to defeat every enemy while preventing them from killing the defenseless Tiki. What makes it harder than most other Escort Missions in FE is that the enemies will completely ignore you unless there's no other way to get to Tiki, and enemy reinforcements just keep on coming for several waves from all around you. By the end, it's perfectly possible to be seeing a huge mess of Risen surrounding your army as you hold them back as best you can while you wonder when in Naga's name will they tire of throwing themselves at you.