Majeh tends to walk around casually pulling off awesome moments, so the highlights should only be covered in his case.
His first appearance and subsequent defeat of a rampaging demon. Casually. Without any effort. A very fine Establishing Character Moment, as it shows just how Badass the main character is.
Speaking of casual, Majeh's way of passing the entrance test into the Martial Arts tournament: crumbling granite with hisfingers.
His first fight in the Martial Arts tournament in Nakyang. At first Majeh is playing easy on the guy; then Samhuk provokes him and Majeh oneshots his opponent.
Dohwa's first appearance. Taking down the Insane Hounds effortlessly with needles and casually insulting them along the way.
Not to mention her final fight with them. At first she's not taking them seriously at all, then they manage to hit a Berserk Button. Cue her introducing them to the Oosajejoo family's poison capsule and taking them out with a rain of sleeping potion dipped needles. Not to mention the nearby civilians as well by accident.