Vergil is, first and foremost, a first-generation Cambion, a half-devil, son of the Legendary Dark Knight, Sparda. His blood, his lineage, already ensures that he stands above common men by principle, able to deal out and withstand hits that would destroy boulders with almost contemptuous ease. Much like his brother, Dante, his physiology allows him to withstand wounds that would be fatal for a normal human, such as a bullet to the head or a sword to his chest, and heal from them in what is nothing short of regeneration, so long as said wounds are not the result of magical weapons specifically made to fight against the supernatural, although even that his hard-pressed to damage him, and it can be said that only the strongest magical weapons can truly wound him, although he will be overwhelmed by mundane weapons so long as they pack enough punch or their numbers eventually overwhelm his regeneration.
Vergil is incredibly fast, able to cut bullets mid-air in a casual display of speed, and keep up with his brother, who displays the same feats. Another example of his speed is ability with his weapon of choice, the Devil Blade Yamato, with a slash from him being so quick that his enemies do not realize they have been cut until they fall into pieces after he seathes the blade.
He is also an expert in the Iaido-style of swordsmanship, centered around using the scabbard to block or parry, then unseathe the sword for a lightning-fast counter before returning the blade to the seath, where it will wait until the next time it is needed. He can use other styles, as well as other types of weaponry, but due to his preference for ending battles in a single stroke, he sticks to Iaido.
As far as esoteric abilities go, he is also a superb user of what is commonly referred to as Dark Slayer style, which centers around teleporting around the enemy, striking, then teleporting to another spot almost immediately thereafter in order to dodge and confuse enemies. The limits of this teleportation range to, at most, six to seven meters, so it is not useful out of combat.
He also posesses skill with Summoned Swords. These ethereal blue blades can be used in a variety of manners: either traditionally as 'bullets', so to speak, able to move at great speeds, or they may be organized into patterns around the user, such as a circle to protect him, or teleported to spin around the enemy for a scant few instants before stopping and launching towards the center, closing off nearly all venues of escape save for jumping if the enemy in question can react before being skewered. It should've noted that, although they can kill humans with ease, devils and supernaturals are hardy by nature and, as such, far more likely to shrug off all but the greatest barrages, although most tend to, at least, be momentarily slowed down.
Finally, Vergil posesses what is commonly referred to as Devil Trigger. In this state, he sheds his human appearance for a short time and takes on an appearance befitting his heritage, making it so that all his attributes, even his regeneration, are boosted to absurd levels, becoming able to shrug off and heal from nearly any sort of attack in a scant few seconds, as well as dealing further damage with each attack due to his augmented strength and reaching godly levels of speed. It should be noted that his coat becomes a part of himself, able to turn into a pair of leathery wings he uses to fly. Another thing to note is that each use is quite energy-intensive, so he will be exhausted for a time after he returns to his normal state. Fitting, given its nature as a trump card.