How do I kill Anti-Fairies?

You can get the Magic Powder from the witch's house north of Kakariko (before you enter the Eastern Palace):

Head back to the main part of Kakariko Village and go all the way up and out of the village. Head right to the next screen. Continue going right to the next screen. Keep going right another screen. Pass through the graveyard to the next screen. Go down a screen and cross the bridge. After the bridge go up a screen after killing the enemies and cutting through the bushes. Make a right here. Go up and give the mushroom to the witch just outside of the shop. Afterwords, head left a screen and return back to the witch. Go inside the shop and the magic powder will be waiting for you. Talk to the guy in there to fill up your hearts. Exit the shop. _(source)