This boss is a bigger and more dangerous version of the pentagon enemy, almost continuously shooting at you with partially homing bullets. Another difference is it will go after you if you get close enough, so you may want to keep your distance.
Strategy 1 - Using the default fireball
Not an ideal weapon since most of your bullets will be destroyed by enemy bullets while you shoot at each other. The best strategy is to keep your distance from the boss and dodge its bullets, waiting for a little gap of time between the boss' shooting bursts. Then use this short period of time for payback!
Strategy 2 - Using a the boomerang
Like the shuriken this is a weapon that does not get destroyed when hitting an enemy or an enemy's bullet. The boomerang can also cause double damage if the enemy gets hit both on the initial shot and on the way back, so definitely a good choice for this boss. In any case, and to make your life easier, you can also wait for the gaps between the boss' shooting bursts to prepare power shots and deal extra damage.