You can't be an evil overlord without powers. Luckily for Walter, he has an entire bag of tricks that he's happy to unleash on unsuspecting humans. Some are new, while some should be very familiar to longtime Castlevania fans...
Walter has a range of attacks that he uses in his epic battle with the player. Here's some images, descriptions, and a little extra information about each.
key to attack notes
GB = guard break (can be blocked by a perfect guard)
FE = attack is fire element
SP = special attack (restores MP when blocked)
Okay, this isn't an attack, but the only time we see Walter teleport is in battle. He'll pop in and out to set up attacks and to avoid being hit. Later, Dracula uses the same ability against his opponents.
beat down [GB]
As you'd imagine, this is Walter laying the physical smackdown on his opponent. Walter fights with his fists, an unexpected and barbaric move from the vampire who has put on an air of elegance.
hellfire [GB, FE]
Hellfire is mysteriously not the signature triple fireball attack, though Walter does use that attack. Instead, his hellfire is a pair of white energy streaks that home in on their target. These are pretty hard to dodge, especially if you're playing as Leon.
dark inferno [GB, FE]
This is the three fireball attack. Walter lets out three large orbs of fire that travel a short distance before exploding. Very easy to avoid, as he pauses to use this attack and the fireballs move slowly.
shadow inferno [SP]
Just like dark inferno, but there's only one fireball and it's purple. You want to see this one used; block the explosion to recover MP. Thanks, Wally! :D
mana flare [GB, FE]
This is almost as annoying as hellfire. Light will gather on the floor and start to follow the player, shooting up spikes of white light as it goes. Best avoided by rolling or dashing away so it can't catch up.
demonic megido [FE]
The mother of all attacks, this is Walter's version of a nuke. If you see him backing up to the throne at the far end of the room and staying there, back the hell up as fast as possible (pressed up against the door is best). He'll rise into the air and transform into a demon that looks suspiciously familiar... like Dracula at the end of Rondo. Once transformed, Walter releases a HUGE fireball that fills the entire room, except for the hiding place by the door. I've heard mixed things about if this attack can be perfect guarded or not; the Japanese perfect guide says no, and I sure as hell haven't tried it myself. Knock yourself out.
Megiddo, by the way, is a hill in Israel that rests at a crossroads of several ancient trade routes. As such, it was the site of several major battles throughout history. The word armageddon may refer to the hill, which is called Har Megido (mountain of Megido) in Hebrew.
Walter has at least one other power that isn't used in the battle: mind control. In the scene where he meets Leon and returns Sara, he attempts to use this power on Leon, but fails. It seems that Leon is protected by either his own strength of will or the magic of Rinaldo's alchemy that enchanted his whip and gauntlet. Sara, however, is charmed by the spell and cannot call out to Leon even when he appears before her.