Sokudo mode is key. You must go fast. Use your speed as a tool. For the most difficult circular projectile patterns, you want to go in a circle opposite to the circle direction and wave up and down. Practice doing this, then in your full run, go in a fast circle. Remember, for the final boss, use
for the orange ball and fire plain purple bullets with
for the purple ball. Following these tips, you should be able to complete this level with ease.