First of all, the weakness for this boss is the Rakukojin (Metal Shark Player's weapon). The best way to inflict damage on the boss is to do one or two jump slash attacks as the core is coming out, then jumping, rakukojin attack, get hit, rakukojin attack, then double jump, rakukojin attack, and repeat, you should be able to destroy each core in one go (if you get a good pattern). Also, when you destroy one core, attempt to attack the other one as it is going back inside of the big blob thing. This speeds up the rate of the movement in between cycles, which saves a nice amount of time. Example video of a good fight: