Honestly if Taylor is to 'kill' Leviathan, one of the more believable ways is to have Leviathan be Clockblocker'd first, since Switchblade should be able to cut Leviathan to shreds while it is under a time lock. Endbringer fights does not always have to go in the direction of the main character soloing said Endbringer after all.
Wouldn't she have to know it existed to kill it, though? If not even Tattletale can be sure it's a real thing 70% through canon or whatever, I doubt she's gonna decide it's a thing here.
I don't believe Shiki has ever cut anything in canon that she is not aware of beforehand. So unless Tattletale brings up something that prompts her to
look for a connection between Leviathan and Eidolon, she shouldn't be able to see its lines. We didn't see Taylor displaying otherwise either, since she is aware of Bakuda's dead man's switch before she
saw and cut them.
Unless of course, Taylor turns out to have Shiki Tohno's Pure Eyes on top of Shiki Ryougi's MEoDP, but I highly doubt that is the case.
Just because Taylor does not get hurt by the explosions does not make her necessarily faster than them, rather, it means she is able to avoid their effects---whether by speed or some other means is merely a detail of execution.
This.
My money is on short range teleportation, seeing how in that scene Shiki was on the ground, in midstep, facing away from the explosion's center, had her dominant hand occupied with a phone and her blade sheathed even after the bomb had exploded, and somehow ended up untouched 10 or so meters in the air despite that.
Moving away from this clusterfuck of a debate over speed (Servant Ryougi has A+ Agility in FGO by the way), if I'm not mistaken, cutting a tsunami wouldn't actually make the wave disappear or anything, it would just negate any damages it was about to cause. Somehow.
Well, in KnK's canon Shiki cutting the future where she gets killed by a bomb somehow makes it so that the bombs in that parking lot would not explode until Shiki is clear of the danger zone. Dunno how it applies to Shiki Ryougi's power, but with Shiki Tohno stabbing the point of an object renders it no longer able to affect anything, while cutting it still leaves the main body alive.
If I'm not mistaken Taylor's MEoDP are the same as Ryougi Skiki's, and since Ryougi's eyes run on the idea of "if it exists I can kill it" then I believe Taylor can see Levi's connection. I mean Ryougi did say that with her eyes she'd be able to kill God if he existed, her (almost) exact words if I remember correctly.
She can kill the distance between them.
I'm not joking
'If it's alive, I can kill it', actually, the same as Shiki Tohno, but with the requirements of what qualifies as 'alive' being really, really loose (i.e ghosts qualifying as alive to her). The example given by WoG is that Shiki can cut a telephone pole because it counts as alive to her, but that she cannot see lines on a broken telephone pole because to her it qualifies as dead. It is also by WoG that Shiki cannot kill god even if it exists due to it in the Nasuverse being an existence that is neither alive nor dead.
Her being able to cut distance is most likely fanon, and if it isn't I have certainly not find proof otherwise. The only reason she is able to cut the 'future' in Mirai Fuukin is because said future was given form by Mitsuru, and that the future is normally invincible because it had no form. That same logic might apply to space, time, friendship, conflict, etc. since those two do not normally have a form unless if is given one (i.e. time bubbles and distorted space).
There is a claim on her being able to cut distance on the Versus Wiki, but it is naturally uncited, and even then attributed to only Void Shiki and not regular Shiki Ryougi. Void Shiki shouldn't apply to Taylor, at least for now, especially since Void Shiki's abilities is not so much her using the MEoDP so much as her using the thing that gave her the MEoDP.
Of course, Mystic Eyes in KnK and Tsukihime work based on how their user perceives things, so Taylor
might still be able to cut distance if she is more suited to perceiving and killing those sort of concepts than Ryougi is.