I have come across 2 locations so far where I’ve seen what looks like a female koopa with a red hat. Whenever I get close she runs off. I’ve hit her with the hat several times, but it just goes right through her. What is the point in this? Is there a way to catch her?
Yes, you need to go up to her as a regular Koopa. There will always be some Koopas in the area, usually more than one. You will often need to stack all of the Koopas on top of each other and make your way to the female one. Once you get close to her as a Koopa, she will fall in love and drop a power moon.