Combat model changed in DA.
Important things to note are as follows:
All ships fire at least the first round in a combat now, even if they're destroyed in the first hit.
Each weapon on a ship fires once per round of combat.
Tie rule added; if both ships/fleets destroy each other after 50 (ship) or 300 (fleet) rounds of combat, the ship/fleet with the highest attack survives with 1 hp.
Given the above, your best bet would seem to be a fleet full of fighters-more than he has weapons. As from your comments on IRC it would seem the DL ship has approximately 20 weapons mounted on it, you're looking at using tiny hulls, as small at 3 logistics each won't give you enough ships.
Alternatively, if you can build a huge hulled ship yourself with more attack (339?), it should/would win, and probably survive with only 1 hp. It would only need approximately 14 black hole eruptors/nightmare torpedoes (DL/DA name vs. TA name), but I don't know what your tech level is. Alternatively, 16 doom rays should get the job done. This is assuming you have no military resources, however, so adjust that down if you do.
As a note, psyonic beam isn't sufficient for this task. Mass drivers are irrelevant for our purposes because you stated in IRC that you were using beam and missile, but it would take 22 of them for our purposes.
Look here for more info.
As I have not yet bothered to complete the campaign in DA or TA, I can only offer suggestions rather than recommendations, based largely on the contents of the wiki. I'll leave the latter to other posters who have experience with it, but please do give my included suggestions a try and report back.
