Dante can make something as mundane as getting dressed look badass, performing a series of mid-air acrobatics while under the attack of a 15 foot tall demon. His nonchalant "missed" afterwards serves to establish that although this Dante is different, he's still definitely a badass.
The Bob Barbas boss fight. Even fans who dislike the game praise this particular battle and for good reason. It's a battle against a demonicBill O'Reillyhead in a cyber-realm, and at several points in the battle, he teleports Dante into news broadcasts where you have to battle his demon minions (or, as Bob calls them, "innocent citizens") while he reports on the so-called terrorist threat presented by Dante and the Order.
Dante and Vergil's killing of Mundus, ending in a Clean Cut from Rebellion that cuts Mundus in two, followed by him exploding!
Dante slugging Vergil in the face during their battle.
For that matter, the entire final battle against Vergil. Dramatic Thunder, a tricky enemy Dante's size, teleportation, and a Doppleganger Attack. On the harder difficulties, you feel like a badass for winning.
Not just any Dramatic Thunder. The fight starts with the skies perfectly clear. The thunder clouds build from the ground up at the edge of the arena, and by the time the fight culminates, a snowstorm has occurred and has coated the ground. The cutscenes throughout the fight make it clear it was Dante and Vergil's growing power that caused it.
The AI was reworked in the Definitive Edition, which definitely made Vergil more difficult. And gets even crazier with the Hardcore Mode perk.
Dante gets his white hair. After all the criticism about the new Dante's character design, the fans got their wish.
The ending of Vergil's Downfall. An army of demons approaches Vergil, ready to tear him apart. Vergil, fresh from destroying the last remnants of doubt and goodness in his heart, turns around and his eyes briefly flash red as he prepares to draw his sword. The demons are so cowed by his new terrifying power and resolve that they immediately bow before him.
While the game's enemies are only somewhere between competent and being punching bags, Drekavac and the Dreamrunners are by far the game's most badass adversaries outside of the bosses. They can deflect attacks, teleport, leave very little opportunity for counterattack, and can deflect all gunfire by twirling their blades. Also they dual-wield Katanas.