Gradius III is the most difficult game I've played in recent memory, hell, maybe in my life. I understand it was originally an arcade game, and I suppose that making the game so difficult would allow for more quarters to be pumped into the game, increasing revenue for the arcade operator.
But Gradius III is INSANELY hard, even more so than Gradius and Gradius II. There are so many situations in which the entire screen is full of bullets, and the only safe spots are spaces that are barely the size of your ship. At least in Ikaruga everything happens the same each time, so you could memorize patterns. This does not apply to Gradius III.
I've been working my way through Gradius Collection on the PSP for over a year and a half, playing it occasionally. I think it took me around eight hours over three days to beat the Stage 3 boss in Gradius III, Big Core MK III, even though it's obvious what needs to be done. You'll need to position yourself in between the initial diamond/crisscrossing lasers, which I was able to do consistently after some practice. After taking some damage, the boss will switch to shooting a wall of lasers, and the only safe spot is the gap between the shots.
The Stage 5 boss, Vaif, was also frustrating, and it took me another couple of sessions over two days to beat him. So for anyone who needs a strategy for this boss, here's mine. You'll need a few options and missiles/smart bombs, and working quickly is essential.
As you move into the boss area, move to the left side of the screen and position your options below you. This will allow you to take out the bottom left Moai quickly. The next Moai to open is the top right one. Move up next to the top middle Moai and shoot it out quickly. The next one to open is the top left, but you can't attack it just yet. Position yourself to take out the next Moai to open, with is the bottom right one, with either your missiles or lasers. While you're doing all this, eliminate the smaller Moai heads that the bigger ones shoot when you can.
Assuming you've worked quickly, at this point, you have three Moai gone. The only ones left are the top and bottom middle ones and the top left one. The top middle one is the next one to open, which is your next priority. Up until now, the smaller Moai heads haven't been too much of a problem. This will change, because more and more of them are being released, so you'll need a new strategy to avoid them. When they are released, move in a clockwise direction around the screen. You don't want to shoot them, since they expand, until you are back on the left side of the screen. You'll only have a short time after eliminating them to focus your fire on the top middle Moai. If you're lucky, while you're taking this one out, you'll also get the bottom one with your missiles.
When the only remaining Moai is the top left one, he will shoot out four smaller Moai. Again, move in a clockwise pattern, leading them to the right, and get back to the left to take them down. Now, you want to position your options near the mouth of the Moai, and this may take a few passes, avoiding the Moai's attacks before you succeed.