One of the easier ways for this mission is (as other people have said) make sure you turn up the difficulty from the base normal - I finished this one on Crippling difficulty. While this seems counterintuitive what it really does is make your allies, and non dreadlord enemies more powerful, and actually useful.
I had a bit of luck as well, though, the Torians were a buffer between me and the dreadlords, and during the early-mid game period they retook one of their planets from the Dreadlords - and stole the technology for Black Hole Eruptors. Well I Traded for the weapon and pretty soon I had fleets capable of easily bringing down Dreadlord ships.
On another mission, again painful or crippling difficulty the race that actually wiped the Dreadlords off the map were - the Drengin. I was barely holding my own against the Dreadlords when over the course of a few turns the Drengin decided that since they couldn't get to me (Altarians, Torians, and Arceans in the way) they turned their offensive power on the Dreadlords and punted them off the map.
So try turning up the difficultly and see if your allies and enemies can help you out.