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1) Quote from Alicization Rising, 226:

With a faint 'sha', the ray of light surged out again. If it wasn't for Kirito springing to the left immediately before that, the light would have likely gone through his right leg. The light ray that precariously missed stabbed into the marble floor and once again caused a small explosion. When the light faded, a bright-red hole remained melted into the surface there.

2) Proof of the attack being lightspeed:

Barely any blood could be seen flowing from the wound and Eugeo didn’t think there was much of a drop in his Life, but Kirito fell onto a single knee upon landing. When he focused his eyes hard enough, he saw pale smoke rising around the small hole opened up in his shirt.

(Eugeo observing how the lightbeam pierced Kirito and cauterized the wound)

- ...A hundred and thirty years from now in the past, her eminence, the highest minister, confiscated silver coins and other items made from silver, and commanded glassmakers to create a thousand large panes of glass. They were for an offensive art that required no chanting… an experiment labeled «weaponry» though, you see. The thousand mirrors, lined up to form a half circle in the cathedral’s front yard, reflected the midsummer Solus’s light and focused onto a single spot, bringing forth a pure white inferno. That melted a large rock the size of a man in sheer minutes.

(Fanatio describing her Heaven Piercing Sword)

-

—In the end, the eminent highest minister judged it as requiring too much preparation before it got to a battle-worthy state. However, she mentioned it would be too much of a pity for all of it to go to waste, and with her divine miracles, she gathered every one of the thousand large mirrors, tempered them, and created a single sword. That was this sacred instrument, the «Heaven Piercing Sword». Do you understand, criminal? What pierced through your abdomen and leg was the might of Sun Goddess Solus herself!

(Fanatio describing her Heaven Piercing Sword)

3) Why this is not aimdodging:

A more horrifying detail of that skill was how it contained absolutely no prior movements before the discharge of light, such as accumulating the light or thrusting the sword. At the very least, Eugeo couldn’t guess at when the nonchalantly shifting slender sword would emit the ray of light from his position.

(Eugeo notes how the attack has no charge time)

-

The light spear that concealed an extreme heat hit the mirror created by Kirito’s art ritual and changed it from silver to orange in the blink of an eye.

...

Was deflected at an acute angle and sprung upon Fanatio’s helmet. It shouldn’t have been a predictable move, but as expected of the second integrity knight, the light ray was dodged with a head tilt to the right with reflexes on par with Kirito or higher.

(Fanatio also dodged the light beam while surprised at Kirito creating a mirror to reflect it)

4) The distance the light had to travel and the distance Kirito had to move:

They were engaged in a sword fight at this point but the wording makes it difficult to tell how far apart they are at the exact moment of the feat in question, therefore, I chose to lowball it by a lot.

Kirito height

It must have used up the entire cathedral floor, with the wall on the other end so far away it appeared white and hazy. The bath took up nearly all of the floor area and was halved by the path stretching straight out from where Alice and I stood, but each of them were a pool with a size of fifty meters, or so they appeared to me.

(This is floor 90, and Kirito vs Fanatio happened in floor 50)

For the distance traveled by the light, I just used 100 meters because I'm lazy. Kirito's height is 5ft 6 or 1.6764 meters and scaling that in this picture, his thigh is 0.1163 meters thick. This means he has to move left around that much to dodge it entirely.

5) The calculation (Bear with me here, it's my first time doing a calc)

Speed calc for kirito

Kirito had to move 0.1163 meters to dodge a light beam coming at him from 100 meters away.

Time = Distance / Speed

Light travels 299792458 m/s, crossing the 100 meter distance in 3.33564095e-7 seconds.

Speed = Distance x Time

The calc to the right, courtesy of WolframAlpha shows the result, 348659 m/s or Mach 1016.49854.

6) THE RESULT:

Mach 1016.5 or MASSIVELY HYPERSONIC+ KIRITO.

7) IF I DIDN'T LOWBALL SO MUCH:

If I used the part where they're in close proximity to each other, say 5 meters as a lowball, then the result would be 6973 km/s or Mach 20493 or 0.02326130c or about 2% lightspeed. SUB-RELATIVISTIC KIRITO.

That's 20x higher.

Speed calc for kirito2
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8) TL;DR

Extreme lowball: Mach 1016.5 or Massively Hypersonic+

Reasonable guesstimate: Mach 20493 or Sub-relativistic

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