Emmy giving Jakes' thugs a swift roundhouse kick beatdown.
Emmy roundhouse kicking the criminal apprehended by Grosky, when the former manages to incapacitate the other in Scotland Yard. Bonus points for Grosky and the criminal, who burst in through the goddamn window.
Emmy chasing one Black Raven on the rooftops of the market. This girl is obviously some kind of ninja.
In all fairness, you have to give some credit to that kid who not only easily lept from roof to roof either, but also evaded her before he switched.
The Black Raven, an organization of freaking children expertly running a black market and also doing some pretty decent parkour.
The entire final battle, especially Emmy's contribution.
Inspector Groski sprinting from London to Misthallery. It took Emmy 10 hours on her scooter!
In the flashback to Emmy and the professor's first meeting, Layton is just casually strolling by when he notices an innocent girl about to be sent to jail for theft. One Sherlock Scan later he's gotten the real culprit to confess, understands his reason for it, and calmly takes him back to the store to help him return the shoes he bought. The whole thing lasts about a minute and by the end, everyone's problems are solved without the professor ever doing so much as raising his voice.
Luke showing a surprising amount of detective prowess for a ten-year-old when he hands over a notebook filled with a detailed list of everywhere the specter has attacked. Extra credit for doing this thanks to finding a correlation between places the specter has attacked and the water level in the canals lowering. How many of us would even notice something like that, much less decide to investigate further?
Arianna and Tony's friend (with some help from the market children) breaking the dam to flood the streets and defeat Descole once and for all.