The title is misleading. It's not the greatest air/sea battle at all. It's the entirety of the Central Pacific campaign, beginning with Pearl Harbor, through Coral Sea, Midway, Guadalcanal, the death of Yamamoto, Iwo Jima, Okinawa, and the atomic bombs. No Leyte Gulf though.
The battle of Midway can be summed up in a few words. The US threw everything it had against the Japanese fleet. They all failed until SBDs destroyed three of the four carriers in less than half an hour, and the fourth carrier the next morning.
The Japanese maintained strict radio silence during their approach to Midway. This in itself was enough to arouse suspicion at Allied listening posts. As the sociologist Erving Goffman observed, if you want someone to think that nothing is up, don't stage the situation so that nothing at all is happening, because there's always a LITTLE something up.
Plus points are that British carriers were involved at Okinawa, suppressing air attacks from the southwest. Usually their contribution is skipped over. Allied mistakes and weaknesses are treated lightly, probably because of time limits and because history books are written by winners. If I ever see a film about Midway that describes the fate of the Marines' Brewster Buffaloes, I personally will send the producers a check for fifteen cents.