Yeah. Check point system works.
Once we clear most of the last wave of fighters, the Nyx seem to turn my wingmates to slag, and there's not enough time to take out all of the beam cannons before the Alte Orde or Katana gets turned to slag.
I suppose the first step is just to check F2 and make sure your difficulty's something okay.
Try sending your wingmen out to attack the inbound Carthage fighters (C-3-9) while they're still a little ways out, and holding back yourself with full racks of Slammers or Grimlers. Once you see the Nyxes, focus on them with your missiles, or use C-3-1 to get them down quick.
Alternatively, try holding all your guys way back by the frigates. See if you can pull the Tevs in to a fire pocket.
Once the second strike element jumps in, you really only need to worry about a couple beam cannons - the bow and stern beams on the Iolanthe and Deianira. That's four to Archer. The corvettes should be positioned broadside-on to your approach, so either Archer, Grimler, or Paveway those beams, then pull back, wait for them to roll, and do it again.
Reverse thrust/reverse afterburner is useful for taking out beams but not great for dogfighting.
You can also try switching to a Kent, though I'm not sure how well that'd go.