Shield Special
Call X
(X3 / Xtreme 2)
Zero turns his back towards the camera and teleports away in a red laser. Shortly after X appears in his place, being transported in via a blue laser.
While X3 introduced the concept of switching to Zero, it was in an extremely limited fashion and it wasn't until Xtreme 2 allowed freeform switching.
Neutral Special
Hadangeki (X7) / Denharei (X5) -> Rakuhouha (X4) / Messenkou (C-Flasher) (X5)
Zero slashes down sending a slow moving beam. Pressing the special button again will have him do an upswing, increasing the startup slightly, but also making the blade beam stronger and faster.
With a charge cancel, he'll slam his buster into the ground, firing 5 shots in a fan shape around him.
In BZ, Zero's effects will go from blue to purple and the blade beams will be electrified, doing a bit more hitstun. With a charge cancel, he'll slam his buster into the ground, firing 7 shots in a fan around him.
While Zero has been able to do blade beams since X2, it isn't until X7 that the player could do them and the attack was formally named. Rakuhouha is his giga attack in X4 while Messenkou is what he uses in X5, both being the same move but differently colored. Denharei is just what Nightmare Zero calls his blade beam.
Side Special
Raikousen (X8) -> Mikazukizan (C-Sword) (X5)
Zero dashes forward so fast he turns invisible. He then reappears a set distance forward, lightning tracing his path and stunning any opponents caught in it.
With a charge cancel, he'll then go into a spinning slash that smacks anyone caught in the lightning away.
Raikousen is from the wildly unpopular X7, however it is a key tool in Zero's moveset in the vs Capcom games. Mikazukizan is essentially just Kuuenzan with a visual effect, though here, it would act as a finisher attack.
Down Special
Sougenmu (X5) -> Hayate (W-Shredder) (X5)
Zero gathers up his energy and creates a clone of himself that performs all his attacks on a delay. It lasts a scant 5 seconds and disappears if Zero takes any damage.
If this move is performed with a charge cancel, another clone will be sent forth, attacking with a shippuuga, dashing forward first and then doing a multi-hit slash before disappearing.
Sougenmu in canon functions more like Luma in that it sends the clone out forwards. However, the vs. Capcom games recontextualized it as a clone that follows Zero's actions on a delay which is far more popular. Hayate is essentially just Shippuuga but done by a clone.
Up Special
Hienkyaku (X4) -> Hisuishou (F-Splasher) (X5)
An aerial air-dash. It has no hitbox, but it doesn't leave Zero helpless and can be cancelled out with immediately. It can be aimed straight forward, where it'll be a simple dash, but also upwards where he'll quickly re-airdash to the ground unless he grabs the ledge.
With a charge cancel, he'll follow up with a shoulder tackle air-dash with his body encased in ice, which can alter its angle up or down slightly.
Hienkyaku functions like it does in the vs. Capcom games here where it is a special airdash maneuver rather than source material, which is a normal extension of Zero's movement. Hisuishou is X5's variant which gives it a hitbox.