I stay towards the bottom of the screen to dodge his swoop/hands/rings and lead the missiles along the bottom and up the side. Once his arms are taken out he's relatively harmless (no pun intended).
Edit:
Had to edit my previous post, because, on further playing, I discovered the currently best dodging pattern:
You have to go in the opposite direction of the huge mech, so when he's on the right side and releases his f-and-f volley, you are on the left-bottom side to welcome them.
Once they target your ship and start to fly in your direction, you just move to the right side of the screen, while one missile after another misses your ship. If you reach the end of the screen, while there are still some missiles left, you continue to move up. Then you position yourself on one of the sides of this robot, in order to avoid his flying arms and repeat the whole pattern in the other direction.
My favorite weapon is RED plus Homing Missiles. With any other weapon at full power, you'll only release two missiles at one time. Fully powered RED allows you to release more. It also works flawless on diagonals, so, you just concentrate on dodging the missiles & arms of that boss, the rest is self-acting.