The Rigel Domain was housed in the Large Storage compartment in the Ozymandias' Storage Sector. It was later destroyed by SOAR member Patrick Tyler, prompting MTHR to destroy the entire Storage Sector.
You can kill as many Rigel as you want (and they just keep on coming), you won't lower the boss health bar without directly attacking the Domain itself. This is a very difficult battle.
Equip your Wide-shot (switch to the Heavy Vulcan once that runs out) and the Tempest Wasp. Continually release Wasps (when you run out of one type, switch to another) to help take care of the Rigel swarming the room. You need to focus on attacking the Domain (remember to use the Left Trigger to stay locked on it).
Don't be afraid to shoot down some Rigel in-between wasting the Domain. The Domain has only one form of an attack, aside from spitting out Rigel. That's a spore attack. The sides of the Domain expand and then a spray of deadly spores shoots out. Keep moving at all times and when the spores fly, dash and jump backwards to avoid. This battle is all about persistence.
Once the Domain is dead, head to the computer (which it was hiding in its nether regions) and unlock the door to the Shaft Sector. Enjoy another cut-scene showing off a nasty explosion. Once the cut-scene is finished, you have 40 seconds to run to the door to the left.