The King Bomb is a pain in the ass. Equip a Gambit for using Handkerchiefs so you can get rid of the Oil status. Make sure to get rid of the mini-bombs with Blizzara when King Bomb calls for them. Then just use physical attacks. Keeping Shell on everyone would be a good idea. King Bomb has a really annoying habit of restoring his HP when it gets low. You're best bet there is to blast him with a couple Quickening chains when he starts getting low on HP and hope that kills him.