How in the hell do I beat the Lukara?

I'm on the Downfall mission, fighting the Lukara with a Level 65 Starfleet toon in a Sovereign-class. All my weapons are Level 13 (4x disruptor-tetryon beam mix with +30% consoles on both and 4x quantum torpedoes with +26.2% console). My shields are Level 12. When I start the fight, I use my tachyon beam, high yield torpedo, beam overload, aceton beam, and directed energy modulation, then activate my Delta Quadrant beacon, launch a heavy phaser turret, and launch boarding party shuttles. Occasionally, I'll launch Scorpion fighters. The most I can ever get this SOB down to is about 75% until my Delta Quadrant ships go away and the thing slowly regens back to 100%. I can barely even dent the shields. I might as well be throwing pebbles at the hull until it finally locks onto me and launches its fighters, which I can survive for about 3-4 minutes, at most.

Is anyone else running into the same problem?