Using puzzle solving skills to shoot down unmanned missiles and drones.
That sword vs pipe fight between the Professor and Descole. And when Descole chops down the pipe to size, what does the Professor do? He catches the other half and dual wields! How amazing is that?
The Professor and Luke on the zipline between airships.
Similarly, the rope hanging off the airship later:
Luke: We're not going down THAT are we?!
The Heroic Resolve in one of the final scenes as Layton, Descole, Luke, Emmy and Aurora prepare to sacrifice themselves to stop the golem attack. Turns out Aurora is excluded from being able to stand on the pedestal, so Bronev takes her place. Bonus points to Luke, for being the first to walk to his inevitable death, accepting it as the only way to save the world. He's twelve years old at this point.