This boss is a big version of the triangle enemy, however instead of dropping explosives it drops angry minions in threes. Not dealing with the minions is not an option unless you want your screen full of them in a matter of seconds. For this one we could use any weapon really, the good thing about those that go through enemies is they could take more than one minion in one shot, the bad thing would be that if you miss a shot you won't be able to make another one until the former goes out of the screen.
The boss will get angry at some point and come after you when its health gets low, just make sure it does not have you cornered by then. It should be easily avoidable after that, unless you also add some unfinished minions to the chase :)
Strategy 1 - Using the default fireball
Probably the weakest weapon, but one of the easiest to use. It's best advantages are you can do burst shooting and the shots do not consume as much energy as those from the other weapons. Just make sure you have enough energy to kill all three minions before the next batch comes, and use extra-energy to damage the boss.
Strategy 2 - Using a the homing weapon
This is a weapon that takes some time to get used to, but at least it's the most powerful one. Not the weapon I would recommend to use against this boss, but used right it is actually quite ok. The strategy here is to dispatch two of the minions with one power shot, and the third one with a normal shot. It may be you could even use just three normal shots. Afterwards make sure you deliver a power shot to the boss if you have the energy to do so.