The filter would be a good start. If it has a suction filter or has a suction strainer in the tank, either would cause the pump to struggle to supply oil volume.
When the pump struggles to get enough oil, it causes high vacuum on the suction side of the pump, which can cause air to suck in around the pump seal, the filter canister, or any loose connection that may not leak externally, but allow air to enter the pump.
This starts a viscous cycle. Once air is entering the pump, the air contaminated oil is sent through the hydraulic system and back to the tank, only to be picked up by the pump again, this time with air bubbles already in the oil!
I'm assuming there is no doubt about the oil level being correct.
Also inspect the suction side plumbing of the pump. Look for loose fittings, cracked or rubbed lines, bad orings in the pump and the pump shaft seal. Just because it doesn't leak oil, doesn't mean it's not sucking air.
If there have been any modifications to the hydraulic system, that would be a good place to look. Any oil return lines that may have been added can cause problems if there is no down tube inside the tank to keep the returning oil from carrying bubbles into the oil.