has not been idling properly?

I own a mitsubishi galant GDI 1834 cc. Recently the car has not been idling properly. At start up the car will rev to 2000 rpm and when drive is engage it will drop to 600 rpm. The idle speed will then fluctuate and it will shut down, it is even worse if the AC is on. It constantly shuts down but will restart immediately. I had it checked and I was advised to change the air flow sensor and the oxygen sensor and clean the throttle body including the idle sensor. I have done all these things but the problem persists. Is it the high pressure pump on the engine head? The car accelerates fine on high speed and there is no reading on the scan tool for the pump. Please advise