We could always just claim it as possibly part of this king power we gained.
After all we only found out about it when Tomoe revealed it to us— which was just a few minutes ago in quest time. Jennifer has done some blatantly superhuman stuff, we could just be tapping into a slight bit of that power without actually knowing how. At least it could be a working theory to explain to Kaleido about why we did superhuman stuff.
On the other hand, this is dangerous precisely because we don't know how to activate it, and more importantly it seems like there is a vocal component that we never did.
Perhaps unconcious ki usage could be a possible explanation?
Or we could go for refuge in audacity "Of course a normal person isn't as strong as me, I'm the king after all! Doesn't mean I'm magical, just that I worked harder for my strength." In which we have super strength/durability but we act like our own ego has blinded us to the fact that it is abnormal. An interesting blend of egotistical and blind to our own ability.
Perhaps we very well could just go and admit to being a Daemon of Pride, and lied to prevent a confrontation against Kui. Perhaps make the "adequate Sinners" vs "great sinners" comparison I mentioned in an earlier post here:
As an aside, when they do find out we're a daemon, if it is not at a time where it is best to off them, I'd kind of like to convince them that we are a different class of daemon than the Kagemusha. That they are simply adequate sinners, reveling in sin, and drawing strength in it at exclusion of their virtues, erasing their virtues to become a hollow shell full of sin. On the other hand, we are a great sinner, and instead infuse even our virtue in sin, and in doing so enhance both. We are proud of our diligence, and because of our diligence we have worked hard enough to be something to be proud in. from there move on to other virtues that might fall in line with how we have presented ourselves to them "We are proud of our patience and because we have that patience, we haven't foolishly rushed beyond what we are capable of, avoiding useless shame," etc, etc.
as an explanation, whether truthful or not about why Daemon's truly do tend towards evil, but is not necessarily so.
That said, putting aside the possiblity of describing any supernatural acts.
We could probably just honestly explain what happened to Kaleido:
1. Tomoe called us here, revealed this mysterious king stuff, and asked us to join her as an underling.
2. We refused to be an underling, but offered to be allies. She decided to kill us for our refusal.
3. Jennifer interfered, it seems like they had a grudge against each other and decided to fight.
4. Jennifer was put in a situation of either living and having her allies be killed, or dying and saving her allies so we attempted to stop that and get them to become allies… by joining the true king together.
5. Tomoe, once again, refused to see wisdom and tried to kill both of us.
While the end of point 4 is a bit iffy, it is iffy in a Victor-like way. A failure because of his own "delusion" of being king, that was just reinforced by these new unknown king powers. I think Kaleido wouldn't think worse of us for it because she already knows that aspect of our personality.
We can easily explain the sword by the fact that someone tried to kill us just yesterday so we brought it along to be prepared for a repeat attempt.
The fact that we didn't start the fight, and only stepped in when one of them was about to die Jennifer's life it should put us firmly in the "good" side of things, without lying once.
If Jennifer has done horrible things to Tomoe in the past, we didn't have the context for it, so if that is found out, we didn't know, and from our perspective Jen stepped in to save us so Kaleido couldn't really blame us if Jennifer is actually the eviler of the two.
Of course explanations only come after saving Jennifer.
[X] Improvise!
-[X] Use the distraction Kaleido provided to rush to Jennifer's side, put your hand between her neck and the sword, reinforcing it just so you don't get hurt, give the non-executive a kick in the nuts to send him off, grab Jennifer and GET THE HELL OUT tactically withdraw.
-[X] Point at the downed executives and shout "Help them!" to Kaleido.
-[X] Watch out for a surprise attack from Tomoe.
If Kaleido didn't specialize in " truly horrific amounts of destruction and in weird dimensional shenanigans", I'd be worried about leaving her there, but she probably got it covered. I am somewhat worried about Tomoe actually talking to Kaleido and explaining her perspective, which we understand very little of. That said, seeing how we knew nothing of either of their pasts and Tomoe was getting ready to kill us after turning down her offer, despite us still
offering to be allies, (before Jennifer actually entered the scene), the events that follow are kind of unambiguously her fault from our perspective and I think Kaleido would realize that if she let us actually explain things if Tomoe manages to temporarily get her on her side.
Since we have a way of actually contact Kaleido that she gave us (doorjam of closet of rooftop stairwell), as long as we try to contact her as soon as Jennifer is safe or dead, things should go well enough.