He was suffering from a sickness as well as the heart attacks, which could take a HUGE toll on his stamina, defense, speed and attack. His power was not at its peak, which both akainu and sengoku mentioned during the fight. In WB peak he had the attack potenial to destroy the world, even if we dont take that at face value I think it would be fair to say that he could at least destory an entire island by himself (since garp was a mountain buster and Chinjo could split an island in half), Yet WB in his sick state couldnt even completely destroy Marineford.
Yet, Im sure there are more people who cant see how Akainu would hurt or KO Big Mom. She literally has been shown to be immune to damage (even powerful Haki based attacks). So any way you imagine Akainu hurting her is probably contradictory to the manga. Im not going to reiterate on how BM is basically the incredible hulk combined with the avatar, but basically she has more ways to take down Akainu than he has to take her down, plus she has an aerial advantage.
And to your point of her not being able to stay on a volcanic island, I would imaine a yonko capable of having the stamina for a long battle considering we have seen people of lesser strength accomplish similar feats. Also, that island would be controlled by Big Mom by the end of the 1st day which would be a major disadvantage to akainu. The rocks, the ground, the water around the island, the sky, the volcanoe itself.... She would give life to all of it to serve her. This feat has already been shown in Manga.