At the very beginning, Big Boss throws his cigar on the floor before he stands up to parajump. He then takes an single step towards the hatch, extinguishing the cigar as it flies towards the door. Awesome!
Snake isn't the only one here, everytime The Boss appears is a Crowning Moment of Awesome for her, successively topping the previous ones. And the battle against The End is a Crowning Moment of Awesome for the series in general.
For example, while in MGS4 Big Boss prevents Snake from firing his Operator pistol at close range pistol during the final graveyard scene, in MGS3 when The Boss and the future Big Boss (then Naked Snake) have a confrontation, during her weapon grab she actually disassembles his M1911A1, and only after he draws it does he realize that she left him only the frame (including the grip) and took the barrel, slide, and probably the other internal components with her.
For an outstanding example of how much respect she commands, when the gigantic sadist Colonel Volgin questioned her loyalty, all it took was her walking towards him to have him reel-back in fear and apology. That's right, folks; a Physical God of Thunder who can punch through steel and wipe out batallions with a wave of his hand is terrified of this warrior half his size, who is all but normal if not for her mastery of martial arts. A true Lady of War if there ever was one.
What's even more impressive is that The Boss has her single greatest crowning moment of awesome posthumously!
Despite being a straight male, Big Boss's crowning moment of awesome was the Ho Yay Revolver Ocelot. He was so Bad AssEven the Guys Want Him, WITHOUT REALIZING IT. (Not coincidentally, when he left the Patriots, both EVA/Big Mama and Ocelot sided with him.)
Then again, that latter was almost certainly an allusion to the unignorable difference between those who coordinate military actions from a comparative emotional distance and those who actually fight in the field. No matter how much Sigint and Paramedic liked Snake/Big Boss, it wasn't the same as what the other two went through with him.
Also from MGS3, the entire fortress escape. You ride in the sidecar on EVA's bike, gunning down countless soldiers (and pursuing bikers), all while Colonel Volgin chases you relentlessly in the Shagohod. And the boss battle against it that follows. It's a Crowning Moment for just about everyone involved.
It's this troper's belief that anything to do with EVA's bike is crowning moment of awesome, particularly when she backflipped off a ledge onto said bike and then proceeded to drive it up young Ocelot's FACE. (And yes, Ocelot DID end up with tire tracks on his face for the rest of the scene.)
At a certain point in the final fight against The Boss, "Snake Eater" begins playing, leaving the player in a difficult fight set to a massive, overzealously fun shoutout to stereotypical Cold War spy films.