Akainu was nominated for the position of fleet admiral after Sengoku had retired. Kuzan, however, was against the idea of having him become the new fleet admiral and the two admirals battled each other for the position on Punk Hazard.
The battle on Punk Hazard between Akainu and Kuzan has never been shown.
After his duel on Punk Hazard, Kuzan received several burn scars spanning from the right side of his neck down to his entire right shoulder and onto his torso. His right hand is also heavily scarred and most noticeably he’s lost part of his left leg, for which he now wears a prosthesis made of ice formed from his Devil Fruit ability.