Just for kicks, here's the full procedure...
- The Cuckoo Lady in Kakariko Village will give you an egg which will hatch with new daylight. Use the chicken to wake up Talon, in the house by the steps to Death Mountain. Return the chicken afterward, and the Lady will give you a blue rooster, Cojiro.
- Take Cojiro to the Skull Kid's post in the Lost Woods, where a boy is sleeping. He'll trade the bird for a Mushroom.
- Hop on Epona, and ride quickly back to Kakariko Village. An old witch lives behind the potion shop; she'll make a potion from the Mushroom.
- Return to the Lost Woods, and a Kokiri girl will be where the Skull Kid was. She'll give you the Carpenter's Saw.
- Visit the Head Carpenter in Gerudo Valley (you'll need to jump the broken bridge with Epona). He'll give you the Broken Goron's Sword.
- The giant Biggoron lives on the top of Death Mountain. When you show him the Sword, he'll give you a Prescription.
- Use a bottle of Blue Fire on King Zora at his domain, to release him from Red Ice. He'll give you a Bullfrog.
- Race to Lake Hylia on Epona's back, and show the Bullfrog to the Lab Scientist. He'll give you some Eye Drops.
- Race back to the top of Death Mountain in less than 4 minutes, and give the drops to Biggoron. He'll award you a Claim Check, and ask you to return in a few days.
- Wait three days, or play the Sun's Song six times, and show the Claim Check to Biggoron. He'll give you the finished and unbreakable Biggoron's Sword.