Time Lords and Terror/Awesome

THE Crowning Moment of Awesome in the story is when the mane six, gentle and passive creatures that they are, confront that Eldritch Abomination the S'muz. It should be a total Curb Stomp Battle, with the cosmic horror reducing the mane six to gibbering madness before devouring their bodies and souls. Instead they call upon their Elements of Harmony and send it sobbing for home to escape the wicked, horrible ponies, pleading for its misbegotten life the whole way. Take That, Yog-Sothoth!
A good second runner up is Twilight Sparkle verbally slapping The Doctor upside the head when he explains his final option for defeating The S'Müz

Twilight: I said shut up! In case you’ve forgotten this is our world! These are our people! What the hell gives you the right to tell us that we can’t fight for our home, for our lives?! You’ve only been here a day…less! How dare you just put on a brave face and tell us to go hide behinds the sofa while you, The Doctor, go gallivanting off to stop the cosmic monstrosity or destroy our universe trying?! What in Celestia’s wide world of magic makes you think I’d let you?!”
The Doctor opened his mouth to say something before snapping it shut again.
“Now.” said Twilight. “You are going to help us, and we are going to help you. We are going to get through this without any deaths, sacrifices, tragedies, or losses. We are going to stop the Carrionites and the S’Müz together. Understood?” The Doctor stood silent for a moment, Twilight maintaining intense eye contact with him. “Understood?”.

Early on, when it's first discovered by the ponies that the Doctor is an alien, the local doctor wants to keep him for study and experimentation. When Twilight refuses to allow that and the pony doctor protests, Twilight points out that she's Celestia's personal student and can therefore make life very unpleasant for the pony doctor if she doesn't let the Doctor go. The pony doctor immediately backs down. Rainbow Dash is suitably impressed by the display.