That's very intresting. He has both armor skipping and shield skipping weapons. Here we have an example of a problem caused by too many 'special' abilities being too easy to acquire.
Maybe you need to visit the other thread talking about how races with special abilities need to have a disadvantage when researching other 'standard' technologies?
But setting aside the game design implications, this sounds like a situation where you need to radically change tactics. There are other considerations than special weapon abilities at the strategic level. Are mines available in this game? Especially when placed at warp points they can be very effective. Might be a good idea to spend some research on those. I'd suggest a switch to fighter tactics, but if he's got enough PDC to make missile attacks useless he'll be quite devastating against fighters, too. Do you have stealth armor or cloaking yet? Build some cloaked ships and try to slip into his systems and raid his colonies, damaging his economic base. Think "submarine warfare" for guidelines on how to design cloaked task forces. He can't build these killer ships if he doesn't have the resources to pay for them. On the defense front, you've got to stop letting him dictate the time and place of battle. You've got to think and use old fashioned strategy to out-maneuver him. Concentration of forces can make a technologically inferior enemy superior locally. Find his fleets with your cloaked ships before they can reach your borders and drop mines in their path. Find his ships before they mass into fleets and destroy them piecemeal.