The dragon was in its cave, they entered its cave to - as they admitted - attack and kill the dragon. Shouldn't the dragon automatically be cleared of charges on self defence grounds? Yeah, it killed the attackers, but that's equal force.
While I don't know the exact Japanese used, the English
subjugate does not mean "to kill", it's to either conquer or subdue: in both cases, the outcome would be non-lethal.
In law, we are specific with our words, so this is an important distinction to make.
Since we have no evidence presented thus far that the adventurers came intending lethal force, the prosecution correctly asserts that Diagorm, considering its might, should have been able to repel the adventurers without resorting to lethal force.
The defence is, I believe, angling for the argument that Diagorm did
not, in fact, use lethal force, and that the death is the result of either gross negligence or malice on the part of the adventurers.
Since an important facet is that the prosecution claims that Diagorm
attacked without warning, the attorney's first step is to bring into doubt the credibility of the witnesses, I think, since the bias against Diagorm means they won't take her side in a "he said, she said"; if he undermines the credibility of the witnesses, it'll be easier to get people to give the truth a chance.
Liking this a lot so far, but now I want to read chapter 3 already, aha ha.
EDIT: I looked it up, the Japanese uses 「討伐」, which does mean "to subjugate" but I believe it is a more lethal variant, so I believe it is a fair interpretation to say the adventurers had been sent with the objective of
slaying the dragon, rather than subjugating. However, we must still consider proportionality: was lethal force the
only way to protect herself? She's level 99, couldn't she have dissuaded the adventurers in some other manner by demonstrating the sheer difference in strength?
I think you can successfully argue that a level 99 destruction dragon should be able to make the adventurer party believe they will not be able to defeat her and thus retreat; at the very least, deadly force should only be used if it is the
only way to safeguard one's life, which would be arguable if it occurred after an extended fight in which the adventurers refused to be dissuaded.
tl;dr
You are correct that the adventurers (likely) came with the intent to slay the dragon, but the dragon should first have attempted to dissuade the attackers through non-lethal force and only escalate to lethal force if there are no alternatives.