This mission forces you on a fixed loadout on a Hydra, thankfully you are loaded with 40 Tornadoes, 9 Trebuchets and 5 Cyclops Torpedoes, with the rest of Alpha Wing (which are invincible).
Your first priority is to defend the Cypher while it egresses. If you're on Easy, you only have to focus on bombers. Tell Alpha Wing to cover you, and let Beta, Delta, and Epsilon Wings defend the Cypher, which will basically destroy any other capital ships in its range.
As long as you have sufficient fighters defending the Cypher, you can basically bypass most of the fighters 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. Send two of Alpha Wing to take out the other Lilith (you need to destroy each Beam Cannon, but destroying the ship itself is a secondary objective), while you (and the other Wingman) focus on one.
When the Argentum (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 Argentum is as good as dead. If those threats are dealt with or the Cypher is in safe instance, send all wingmen available to cover the Argentum, while it faces the wrath of several fighters and bombers.
When you get the dialogue cue to clear out of the area, you need to be in three thousand meters of safe distance from the Nyaralathotep when the Argentum finishes its suicide run. When you get clear and are able to sit back, just watch the massive fireworks.
Congrats on completing Derelict... if you managed to pull this operation off. If the Argentum dies... 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.