Yeah, that was a hard one. That nebula forces you to attack, allied support or no. Defence is futile against those colony ships.
This procedure allowed me to win:
Switch to a spire destroyer with 4 plasma siege cannons III and one shield (lights don't matter).
Bring it in, and attack the nearest starbase, protecting yourself with shadow shields.
Then kill the nearest starbase from your current position with the same procedure. By now your sheild will be down and you will have taken heavy damage. Retreat out of the nebula for a quick repair.
Reenter, then kill the last two bases.
I actually managed to win with a way different proceedure:
Human Shadow Destroyer, 3x Mark III Bomber Bays, 3x Laser IIIs and 3x Doom Accelerators IIIs
I got right next to each enemy Starbase, so that every module and my main guns were within range, dropped shadow shields, and moved around under the shadow shield to spread around drones. Regular shields were beyond useless for me this mission; I could never get time for them to recharge. Ultimately, I think I had to get lucky with colony ships choosing the drones rather than my champion or allied ships. My point is that the shield not working made this scenario overly difficult, almost to the point of RNG luck dependent. Oddly enough, the first time I beat the Citadel Ascendant (in trial version, a while back) was by using a Neinzul Champion defensively and repairing starbases. Looking back, I have no idea how I succeeded that time...
Interceptor Drone modules are a good choice, both because of the good damage they deal to the colony ships, but also because of the distraction bonus.
As an alternative, try Armor Polarizers and either Missiles or Rail Clusters.
The Colony Ships have a Light hull-type, so Rail Clusters get their multiplier there, and have excellent multi-target capability.
Missiles, on the other hand, are good at killing the Starbases. You can take your pick of the heavy modules based on your offense/defense preferences.
For small modules, Polarizers are surprisingly good in Nebulas. Mk I Polarizers do about 20,000 DPS to starbases - the best of any Small module - and are equally good against most nebula ships. The colony ships, however, have 0 armor, so Polarizers are not useful against them. So, as an alternative, (I hate to say it) I've found Flak modules work OK (The Colony ships tend to cluster in my experience). Flaks get the multiplier, and get multi-hit.
I prefer either Zenith Cruisers with Missiles and Polarizers (and a shield), or Human Cruisers with HBCs and Lasers or Doom Accelerators, for many of the mid-later Nebula.