At no point is Moya ever seen eating on camera. We must infer, as an organism that lives its entire life in space, it would make sense for her species to subsist off of whatever can be found between stars. I would think new star systems and planetary bodies would be the equivalent of watering holes she would be able to lay over near and recharge.
As such, she should be able to subsist off of the radiation of stars including high energy particles and cosmic rays, x-rays and gamma rays, solar particles and perhaps even hydrogen gas from large gas giants, which are shrouded in such clouds. She might replenish her mass by passing through dust clouds with a high mineral content.
- She does not appear to use solar energy as a primary food source, though it is not said that she couldn't or didn't
- nor is she seen scooping gas from gas giants for raw materials to repair herself or to replace mass.
- This also does not mean she couldn't or didn't only that we didn't see it. No one tuned in to Farscape to watch a Leviathan eat.
She apparently does have a need for a particular type of unobtainium known as "iriscentent fluid" which is used by her power plant and life sustaining systems. It can be found on most sophisticated commerce planets and considered very expensive.
In the premiere episode Rygel tries to sell the Hurlian Stone set into a ring he owned. He tried to sell the ring to a green alien with a bottom jaw that split apart. He wanted 35 barrels of iriscentent fluid, but the alien offered him 20 for it. ("Farscape Premiere")
The material, iriscentent fluid, is mentioned only in passing in episodes where the crew are stopping on commerce planets to resupply. Since she does not appear to need much material to repair or restore herself, she must have a super-efficient bio-mechanical repair system, able to utilize any and all mass on board to repair or replace systems.
After escaping the Peacekeepers, Moya was able to locate this small Commerce Planet in the Uncharted Territories. The Moya's crew was hoping to find supplies in order to make repairs to Moya. Rygel, Zhaan, and Ka D'Argo headed down to the planet and Rygel bartered with a shop owner for barrels of iriscentent fluid.
Since the Leviathans are a constructed race created by the Builders, they may be able to survive on any number of other materials unknown to us. The Builders possessed nearly godlike powers and were capable of living unaided in space in non-corporeal bodies.
The Builders are an ancient and powerful race and are considered by Leviathans to be gods. In fact, the Builders originally constructed Leviathans as ordinary biomechanical ships, only later giving them sentience (souls) and the ability to reproduce on their own.
The source for this very hard to find information was a book called "Investigating Farscape: Uncharted Territories of Sex and Science Fiction" where they list in their glossary of terms, the material called "iriscentent fluid."
The entry is listed as such:
iriscentent fluid: noun - a fluid Moya uses for fuel, and necessary for her functioning.