The Mushroom Cave appears after you take the quest at the bakery. The player must be level 10. It's located above and to the left of the capital on the map, near the coastline.
Theoretically, you can already defeat the first boss. Get a buff at the capital's church, enchant your gear to at least +5, and take a potions just in case.
I had time to check, and healing potions work in battle. I wanted to record a short video, but unfortunately, the power went out in my house, so I'm writing from my phone now.