We had a cry for help on these Boards from someone else some months ago. His problem was an enemy using Crystalline Technology and Phased Energy Weapons in combination. That's ARMOR skipping weapons combined with SHIELD skipping weapons. Nasty. Since the game is already in progress you can't try it out this time around.
But you could research say, the Null Space Cannon and the Phased Polaron Beam if phased shields aren't to close to being developed. That would also be a nasty combination. Since he has the talisman you can skip ECM and other 'defensive' techs (like stealth armor) in favor of piling up as much shield and armor points as possible.
The classic counter to the Talisman though, is long-ranged weapons. Especially seekers. He can't hit you if you aren't in range.