Pocket Egg
As an adult, go to Kakariko Village. Go to the woman near the graveyard. She used to take care of Cuccos. Now, she has a new breed, called Pocket Cuccos. She gives you an egg. In the morining, when it hatches, go to the small house on the ground floor of the village. Talon is fast asleep on the bed. Use the Pocket Cucco to wake him up. Now, take the Cucco back to the lady. She'll be so happy that you made the Cucco happy, that she'll give you another Cucco.
Cojiro
Cojiro is a blue Cucco. It used to belong to the womans brother, but he left, and the Cucco hasn't been happy since. I guess it's time to go find her brother. Go to Lost Woods. Take the first lmeft. There is a mutated man leaning up against a tree stump. Go over to him and pull out Cojiro. The brother will be happy and take Cojiro. He gives you an Odd Mushroom.
Odd Mushroom
Now, there is a time limit on this. If you don't do it, then the mushroom will spoil and you must start again. You CANNOT warp. If you do, the mushroom will go bad. Just run all the way to Kakariko Village. Call Epona if you want. When you get there, go to the potion shop and give the mushroom to the old lady.
Odd Potion
The old lady will prepare potion. Carry it back to the lost woods. The man is gone. Instead, there is now a little Kokiri Girl in his place. Give the potion to her. She will be angry that you took something from the forest. She gives you a carpenters saw that had been dropped in the forest.
Carpenters Saw
Now, go to Gerudo Valley. In the tent, or outside the tent, one or the other is a carpenter. It was him who dropped his saw in kokiri Forest.
Broken Sword
He is relieved that you brought back his saw, but he doesn't have anything to give to you in return, except for a broken Goron Sword. Take the sword and go to Death Mountain Summit. There is a really large Goron here. He was the one that made the broken sword. He is embarrased it broke, but he can't fix it because the sulfuric fumes are hurting his eyes.
Prescription
He gives you a prescription for eye drops. Go to King Zora in Zoras Domain to fill out the prescription. The King doesn't have eye drops, but he does have an eyeball frog which is the main ingrediant for eye drops.
Eyeball Frog
He gives you the Eyeball frog, telling you that if you take it to the lake side laboratory in lake Hylia, the scientist can make the eye drops. So, exit the Domain and the river. Call Epona and ride across Hyrule Field, like the mushroom, the eyeball frog has a time limit on it. When you reach the laboratory, go inside and give the frog to the scientist.
Eye Drops
The scientist gives you eye drops. These too, have a time limit on them. You have to race back to Death mountain Summit as quick as possible. Use Epona to shorten the trip considerably. When you get the eye drops to him, he'll put them in.
Claim Check
Now that his eyes are better, he can work on the broken sword. He gives you a claim check and tells you to come back in three days. If you're patient, wait for the three days to pass, if not, then play sun's song a bunch of times to make the days pass. When three days are up, give him the claim check.
Biggorons Sword
This is what you end up with. It is a giant sword. This is the ultimate sword. Link must use both hands to hold onto this sword. It never breaks no matter how many times you use it.
