I understand that engine driven hydraulic pump noise is caused by several reasons such as cavitation,aeration or mechanical defects but how to troubleshoot this problem using a flowchart from any aircraft troubleshooting manual?
A good mechanic can listen to a noisy pump with a stethoscope and tell whether it is cavitating, has a broken impeller blade, or bad shaft bearings. But the proof is always removal and disassembly. Once the pump is removed, then the mechanic can tell by spinning it by hand whether the bearing balls or races are pitted, and by shaking the drive shaft back and forth whether or not the bearings are beyond their wear limits.
I think the right thing for you to do is ask a real, live powerplant mechanic this question.