The P-39 (among many Allied airplanes) have had several issues that were hampering it's better score vs. Zero.
The crucial thing could easily be the lack of dependable early warning systems in areas where the P-39s were operating during 1942. As seen in ww2 in all theaters, the fighters, no matter how good, need sufficient time to warm-up, take off and climb to the suitable altitude.
Next thing would be the pilot's tactics experience - P-39 should flatly lose the vs. Zero in turning fight, and Zero's pilots were the best in the world in 1942.
Then we go to the engine limitations: the single speed V-1710 was, during the 1st half of the war, a dog above 15000 ft. The airframe issue would be the loopsided layout of the engine intake, much reducing the ram effect. That should steal couple of thousands HP/feet from the already low engine power/altitude. The Japanese bombing runs were conducted at higher altitudes, and their Zeros have had two-speed superchargers, so the Zeros would be the ones to dive at P-39s, not vice versa. Another airframe issue would be the low fuel quantity, giving the P-39 pilot two uneasy choices:
- drop the tank and engage what is close (and that might be the Zero coming to get him), leaving it without fuel to chase speedy Japanese bombers
- leave the drop tank on, and risk to be shot down since one is slow unviedly with the DT
Having the DT attached also lowers the rate of climb, not a good thing if the bombers Zeros are close.