First off you need a mushroom: (dropped by common enemies)
Then you head up until you find a dog (he'll have a mushroom hat or something)
You then equip the mushroom and give it to the dog when the "gift" option appears
After that the dog will follow you
then you'll have to bring him to the cow girl and interact with her, after that a different action will occur and the fight will start
Hope i could help :D
