Katana vs. Predator Claw. Doubly so because it makes up for the unseen blade duels in the first two films. When that scene ended, people in the theater started clapping (though it was more of when the Predator died than when Hanzo did). It becomes especially awesome when you consider that this is the first time EVER that someone fought a peak condition Predator (all others in the series were worn down by the time it got to that stage) 1v1 in melee and beat them, all with two fingers missing. By the way, the actor who played Hanzo knows kendo.
Also take into account that the Predator was armoured, physically colossal compared to him and probably spent its entire life hunting. He was injured, stripped to the waist, in suit trousers and wielding nothing but an old, uncared for (properly, at least) katana, a weapon that needs meticulous care to be effective (to the extent that they often had their own specialist maintenance workers) and only has a single, flexible edge, and was missing three fingers from Yubitsume, a practice specifically intended to make it extremely difficult to use a blade with proficiency. Hanzo showed not only immense skill but the fact that he probably had the biggest, roundest balls of the already awesome group. Imagine how much ass he could have kicked if he had been at peak condition... Those Predators should count themselves lucky.
Royce's final fight with the leader of the Black Predators. Made up of many little Crowning Moments of Awesome. Stopping Edwin, then boobytrapping his body with grenades to hurt the Predator. Using mud plus surrounding the camp with fire to avoid being detected, and then beating the hell out of the Predator with a bone axe. A combination of Dangerously Genre Savvy and sheer badass.
Nikolai vs. the Predators, involving a few claymores... Nikolai spitting in the Predator's eye before blowing both of them up definitely gained him Badass points.
Bilingual bonus as they had him say the nearest equivalent to 'you're one ugly motherfucker' they could find in chechen (actually 'that's quite a snout you have.' to be accurate).
Stans showing enough cunning to wear stolen body armor under his prison outfit, playing dead after getting hit with a plasma caster, and then having the balls to leap on the lead Predator's back and shiv the hell out of him, giving his team time to escape before getting trophy killed. Forget how it's a 'sneak' attack. That is prison battle etiquette, where anything goes. Considering he's got nothing but his shiv, and he's only a little guy, he thoroughly earns his Badass points.
This exchange is so awesome with its execution. Entirely on its own it could give Royce his own prequel:
Edwin: "You came back for us. You really are a good man..." [prepares to stab Royce].
Royce: "No, I'm not." (intercepts the attack and jams the scalpel into Edwin's throat) "But I'm fast."
When the Predators reveal themselves to their prey, and the camera pans around to show them all uncloaking and Alan Silvestri's main theme from the first film finally, gloriously, erupts after many smaller cues earlier in the film. That was the moment the film sealed its status as a worthy successor to the original.
Predator vs. Predator. The original Classic Predator vs. the Modern Black Predator. Despite being malnourished, injured, wielding rather battered equipment, the classic Predator is still able to put up one hell of a fight against the healthy, better-equipped Modern.