How To Finish First Campaign Scenario On Twilight ?

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Greetings everyone. I only play intermittently, so many nuances (and even obvious details) escape me. So . . . I have been playing first campaign mission on Twilight of the Arnor where the task is to destroy the treaty between the Korath and Dreadlords. That is a very generic description.  Am I to influence the Korath out of the treaty? Squash them from the Galaxy? Poison their Cheerios?

I destroyed the Korath and expected to see a mission over screen. No luck. I assume I have to eliminate the Dreadlords from the galaxy next? What is the path, or paths, to victory? I expect that as I play more I will become more accustomed to things, but for now I have no idea.

Thanks for any help.