The Moai boss in Gradius II gave me trouble until I found out an almost fool-proof strategy.
You'll obviously want all 4 options, ripple-laser or the two-way Double, missiles and two speed-ups, maybe one more (depends). What you essentially do is herd the mini-Moais that come after you, slowly moving in a clockwise fashion. Stay somewhat closer to the faces as you circle, but not too close. As you fire you will destroy them and the bullets will be manageable instead of a giant chaotic blanket. Once one of the heads is destroyed, the fight more or less plays itself.
Even if you die, if you learn how to herd the spawned Moais in this way, you should, with a little practice, learn how to time out the fight.