Picking Type 2 is probably the safest bet, but I used Type 3, and pulled it off all right, multiple times without dying.
Type 2 allows you to basically fire in any direction, you may be aware, so if you're using that, just find the pattern the boss moves in before he sets himself up against the right side of the screen, and just clear yourself a path with lasers to stay out of his way. Of course you're dodging those exploding droids, the best you can do there is stay as far away as possible, so when its shots approach you they're spread out more. I basically did the same with Type 3, it's just a little harder, you have to stay really close to the asteroids so your multiples clear you a path through them. I use two speedups, BTW.
Once he sets himself up on the right side, don't fire your weapons, just dodge asteroids coming at you from behind while dodging his bullets (takes a little practice). You may have realized by now that the hit detection zone on your ship is pretty small (like Ikaruga, if you've played that) so you can "brush up" against things like asteroids without dying, although having a shield activated seems to me to expand your zone some. I've been able to ride along certain walls without a shield and have been fine, but if I have a shield activated it'll take it down a notch or two. It's a trade-off I guess.
Anyway, try to position yourself to the left of the big asteroids, they can take quite a few of the bullets from the boss before exploding. The main trick here is to keep moving, wherever you move, the bullets follow. Don't get too close to the left side of the screen, an asteroid can appear from there and smack you without giving you time to move out of the way. Remember, you can move through some pretty tight spots with your ship, and you'll have to here to survive. When the boss' shots end, move to the middle of the screen (vertically) and unload on the core. If you have a setup that allows you to fire backwards, it'll help take care of asteroids that approach you from behind still, that don't get hit by those fire beams. The boss moves up and down a little here also, so try to say in line with the core. It usually took me two full turns to take him out, but Type 3 allows you to move all your multiples in line, so that plus lasers made things go a little quicker. If you don't defeat him, he'll go back to the same stuff as before, just use the same strategy.
Remember, the game has a stage select mode, you can pick any level you've made it up to in the main game, and play with unlimited credits. You can use that to experiment with various weapon types if you like.
Also, you haven't seen anything yet as far as difficulty goes.

What difficulty are you on? I only played through it on normal.
Also, are you aware of the Konami code? It helps with practice mode, since you start at the boss.