Onward to the next level.
This is a little more straightforward and less challenging than the stages you've encountered so far, and you should be able to get through without a lot of trouble. As always, use Rush and the Super Arrow when you ned to alleviate the difficulty of areas. There's not much to say here, just keep moving forward and you'll win.
The boss is a weird flying circular robot. When he opens his sides, he's vulnerable in the "face" that's inside. Fire Gyro Attack in there when he opens up, and repeat until he's dead.