After spending a week, on and off, on the Dread Lords campaign I was finally able to beat the Apocalypse level. In all honesty, &%$@ that mission.
The key is the build lots and lots of small fighters with speed ratings of 6 or more. I gave up on building starbases and went around picking off Dread Lord troop transports while evading the enemy. Make sure you build a custom survey ship that can match the speed of the fighters, as well. When you see the Dread Lords begin to build shields on their ships, switch to mass drivers immediately. They don't seem to ever build shields for them (although who knows, given time).
In order to get an economy going, take over the 7 planets in the corner you are situated in and build up lots of trade centers. Keep the happiness level at about 85% to encourage population growth and by the time the planets reach 2 billion each you should be getting a positive flow of cash.
To win the scenario, its basically attrition; keep the enemy occupied until the friendly AI can take over the Dread Lords. Keep giving them your industrial and combat tech (for money) and the AI should eventually start taking the Dread Lord's planets one by one.
I had beat Apocalypse quite some time ago, and left the DL campaign at Apocalypse, and am now working on advancing my sandbox play up to Masochistic, and dipping a toe into Obscene.
I took all the planets from the Weber system in the north to Markus system in the south, and began developing my economy and technology. I tech-brokered with my allies, giving preference to the Iconians. Soon after the colony rush, the Dreads began sending in 25-Gun Attack transports, taking me by surprise. I responded by buying some 6pc/wk 'Snipe' fighters with 1-Beam Attack, and used the tie-rule to blast 4 transports.
I sent my flagship in the direction the Dread transports had come from, and discovered that they had 4 worlds covered in Industrial Sectors. So as my economy improved, I kept placing more and more spies on their worlds. They tried to fight back by placing spies on my worlds, but I knocked them out with Counter-Espionage Centers.
The Arceans, Altarians and Torians did nothing at all to help(except for buy my tech and go broke), but since the Iconians were holding off the Yor and Drengin quite well, I even gifted them tech or some cash when they were going broke. Up in the far north, meanwhile, the Drath and Korx had become targets of the Dread Lords. The Dread warships were tearing apart every ship they built, yet they sent all their transports in my direction(which kept getting killed).
The Dread Lords then did something that was not too surprising by storyline, but quite surprising in the game: they signed a peace treaty with the Yor Collective! Upon seeing the peace treaty message, I initiated diplomatic negotiations with the Dreads in hope for some tech or temporary peace. They just laughed in my face.
After a while, when my population was up, and my research was going well, the Dread Lords sent more transports towards me. This time they brought warships along as well. I had awesome early-warning capabilities with my Eyes of the Universe, so I managed to snipe all the Transport, but I lost a few of my aging fighters as well. In response, I upgraded all my remaining fighters and built half a dozen extra new-spec QuickSnipe fighters with 4-Missile Attack and 10pc/wk speed. The Dread Lord frigates were left biting dust as their transports were torn down.
Now I had Mk.2 Photonic Torpedoes, Warp Drive 5, Expert Miniaturization, a Hyperion Shrinker, and Large Hulls. With this tech, I rolled out 5 new battleships(whose name I'm forgetting) with 46-Missile Attack and 6 pc/wk speed. The Dread Lords' frigates and escorts got a taste of the tie rule and I steamrolled ~7-8 of them without losing a ship. They brought in a frigate and 3 escorts as reinforcements from the Korx-Drath front, but they got killed as well. I beat them back to their base worlds and knocked out the remains of their military while my troop transports approached. They began building a few defenders with point defenses, but my troops stole the superior Mk.4 HD Spike Driver(!!!) weapon from the Dread Lords to blow their chances. I fitted these Spike Drivers on my battleships, shot down the Dread defenders, and the Dread Lords were soon overrun.