Mihawk x2, GP Usopp, Gaimon, Alvida, Arlong. Leave the Green Pirate Penguin alive on stage 3, stall on him with Gaimon, use Alvida's special to reduce one of the Penguin's hits, stall until you are 2 turns away from both Mihawk specials. Use Gaimon, eat any meat you can while killing the Penguin. Clear the stage as you normally would with Mihawk captains, shaving off HP with specials in the first round, then use Usopp and Alvida to buy time, chaining from Gaimon to Usopp to Alvida to Mihawk to Mihawk to Arlong.
Original writeup is on Reddit
here. It's a really a derivative of Marco x2 and Blackbeard x2 strategies, both of which use similar Gaimon stalling to build specials.