When she jumps on her cauldron, jump up and hit her. She then turns into a frog (you sometimes get hit yourself). when she goes right, do the same. Then go the other way and keep hitting her. When you have defeated her, jump through the mirror.

After going into Begoniax's house you will face her in battle. Here are her attacks:

1. She will swipe elixir at you, which will turn you into a frog for about a minute. To avoid this attack, keep running to the right.
2. She will rise up her pitchfork and run around in circles hitting you. To avoid this attack, stand still and press A at just the correct moment.

To hurt Begoniax you must avoid her elixir swipes, then jump. If done correctly, a red target will appear on the elixir for you to punch. Punch the elixir and Begoniax will turn into a frog. Punch Begoniax while she is a frog and it will lower her health. Repeat this until Begoniax dies.