Lieutenant Mackie and the Cypher crew were right in one thing: The Nyaralathotep is heading home... to the Capellan jump node from Vega, sealed off to prevent a further spread of the Second Shivan Incursion. Now is the only chance to stop the Shivan incursion from continuing on and threatening galactic civilization, meaning the Nyaralathotep and the rest of the Shivan fleet must be destroyed before they open up their new Knossos portal again...
This mission forces you on a fixed loadout on a Hydra, you are loaded with a UD-8 Kayser, plus 40 Tornadoes, 9 Trebuchets and 5 Cyclops Torpedoes, with the rest of Alpha Wing. Beta Wing will consist of Myrmidons, Delta of Erinyes, and Epsilon of Sekhmets.
Your first priority is to defend the Cypher while it egresses. Tell Alpha and Beta Wing to cover you, send Epsilon (which is a ways off) to buy you some time, and Delta to defend the Cypher. The Cypher will have backup, and they will deal with most of the Shivan capital ships in their range.
As long as you have sufficient fighters defending the Cypher, you can basically bypass most of the fighters (on Easy, higher difficulties will have you avoiding missiles like nuts) and focus on destroying the Nyaralathothep's rear Beam Cannon (use your Trebuchets for this, it takes about three or four).
The Liliths are your primary concern. The easiest way to go about this is to use your remaining Trebuchets to take out both beams on one Lilith, and use your Cyclops to take out the other Lilith's beams. As much as you can try to destroy them, you don't have enough time.
If the Cypher has reached safe distance and you're getting chased by the Shivan fighters, tell Delta Team to cover you.
When the Argentus (a Meson Bomb packed freighter on a suicide course for the Nyaralathotep) comes into the scene, you better have damn well dealt with the Liliths or else the Argentus is as good as dead. If those threats are dealt with, send all wingmen available to cover the Argentus, while it faces the wrath of several fighters and bombers.
When you get the dialogue cue to clear out of the area (a burst transmission on your HUD saying "brace for impact"), you need to be in three thousand meters of safe distance from the Nyaralathotep when the Argentus finishes its suicide run. When you get clear and are able to sit back, just watch the massive fireworks. The explosion will destroy the Nyaralathotep, along with both Liliths.
Congrats on completing Derelict... if you managed to pull this operation off. If the Argentus dies before it collides... well, enjoy the dialogue as civilization is doomed from the Sathanas fleet as the node to Capella is opened.
The term "Hail Mary" is used in American football, when the passing team is on a fourth down and on a long distance to the first down marker. Typically, this is a last desperation measure when the clock in the fourth quarter is below half a minute, and the passing team is more than half the field away from the goal, and they need to get either a touchdown or within field goal range to steal the win.