He hasn't learned any new moves, so all that you have to do is avoid his attacks and watch for him to come flying at you with his tongue exposed.

Then use Vine magic to tie his tongue to the overhead hook so that he is hung from it while you hit him with melee attacks and Inferno magic. When Bullhead has taken enough damage, he'll swim to the next island. Guide Nanami over to that new island as Bullhead occasionally leaps out of the water to attack.