Walkthrough: As the fight with Madame Broode commences, she will use her Golden Chain Chomp to try to attack you. Like all other Chain Chomps, you will know its trajectory before it attacks, so use this knowledge to dodge it. As it rushes past you, you must first knock off the hat the Chain Chomp is wearing. After you do, use Cappy to capture the Chain Chomp, which will then send Madame Broode into a fury. Do your best to avoid her swipes, as you be knocked out of the Chain Chomp if she lands one. Keep moving until she tries to bring you in, and then use the tension created to nail her.
As she falls back, make sure to grab the Coins that appear before getting ready to dodge her attack of tossing Chain Chomp at you. You will need to repeat this same process two additional times. Each time you do regain control of the Chain Chomp with the help of Cappy, Madame Broode will swipe more and more at you before getting tired. After hitting Madame Broode in the face three different times, you will win the fight and receive a Multi Moon. Believe it or not, Multi Moons are worth that of three Power Moons!
Before continuing your journey, you can actually backtrack and find more Power Moons. Luckily, more have now appeared: one will be in the first area in Cascade Kingdom, another by the Odyssey Airship by a new Chain Chomp, another by a group of Chain Chomps behind a breakable wall, and even another to the left of the 8-bit wall. After having at least four Power Moons, return to the Odyssey Airship to head to the next Kingdom, the Sand Kingdom.