If Adult Link talks to Anju in Kakariko Village, she will tell him that she has successfully managed to create a new breed of Cucco - one that she can touch without getting an allergic reaction. Thinking that Link might be a good Cucco keeper, she presents him with a Pocket Egg that, when incubated long enough, hatches a Pocket Cucco, which Anju says can be used to awaken a very heavy sleeper. The Pocket Cucco will hatch on the morning of the day after Link receives the egg.
Once the Pocket Cucco has hatched, Link can use it to awaken the sleeping Talon in a house in Kakariko Village. Upon returning to her, Anju is pleased to see that her Pocket Cucco managed to awaken a heavy sleeper and presents Link with a special blue Cucco known as Cojiro, which belonged to her brother, Grog. However, since being separated from Grog, Cojiro has never crowed.
Cojiro will start crowing the next time Link enters the Lost Woods. Grog is resting in a forest clearing to the left of the entrance. He will initially act callous towards Link, but if Link gives him Cojiro, he will be pleased, recognizing Link as a true "nice guy". He requests that Link deliver an Odd Mushroom to Granny in Kakariko Village for him, so that she can make a potion that he needs. However, the Odd Mushroom will be spoiled if taken outside of the Lost Woods for too long, so it must be delivered to Granny within three minutes. (Remember not to warp using the Ocarina, as that will instantly spoil the item.)
Link can enter Granny's Potion Shop in Kakariko Village by passing through the Medicine Shop's back door. Granny will make an Odd Potion (called the Odd Poultice in the Nintendo 3DS version) from the Odd Mushroom, and will ask Link to deliver it to Grog. This section of the quest is untimed, despite Granny's cryptic remarks that her cure will "not work on a monster".
NOTE: If you're playing the N64 version, make sure to use the Mask of Truth to obtain the Deku Nut capacity upgrade from the Forest Stage before proceeding. Due to a bug, this upgrade will be unobtainable after you obtain the Poacher's Saw.
Upon Link's return to the Lost Woods, Grog is nowhere to be found; instead, Fado can be found near the stump where he was sitting. She tells Link that everyone who enters the Lost Woods will eventually become lost and transform into Stalfos. Upon seeing the Odd Potion/Poultice, she insists that Link give it to her, since it was made from materials native to Kokiri Forest, and. In return, she gives Link a Poacher's Saw that Grog left behind.
If Link manages to cross the broken bridge in Gerudo Valley (either with the help of Epona or the Longshot), the Poacher's Saw can be delivered to Mutoh, who is standing outside the carpenters' tent. Mutoh is surprised to see his long-lost tool, and remarks that he thought he had left it behind with his mother (implying that Granny is indeed his mother). He gives Link the Broken Goron's Sword in exchange for the return of his saw.
Death Mountain Summit
On Death Mountain Summit lives the greatest swordsmith in Hyrule, Biggoron. However, since Ganondorf resurrected the evil dragon Volvagia and caused the volcano to be active again, Biggoron's eyes were hit by an eruption, preventing him from seeing. In order to clear his aching eyes, he needs eye drops. He asks Link to deliver a Prescription to King Zora XVI in Zora's Domain.
Talk to King Zora XVI (thaw him out using Blue Fire from the Ice Cavern if you haven't done so yet), and deliver the Prescription to him. Link receives an Eyeball Frog, a creature with many medicinal properties native to Zora's Domain. This is needed for the Eye Drops. However, once taken outside of Zora's Domain, the Eyeball Frog will be spoiled and useless after three minutes. It will also be useless if Link plays a warp song or passes through Death Mountain Crater (the latter due to the intense heat). Link must deliver it to the Lake Scientist in the Lakeside Laboratory near the waters of Lake Hylia.
The Lake Scientist will initially mistake the Eyeball Frog as a present to him, and quickly becomes disappointed when he realizes he will not be able to cook the frog's eyeballs for his dinner. Despite this, he still uses the frog to create the World's Finest Eye Drops for Biggoron. However, since the medicine has no preservatives in it, it will spoil if not delivered within four minutes, or if Link attempts to warp. If that happens, Link will have to go all the way back to King Zora XVI for another Eyeball Frog.
Death Mountain Summit
Link must travel as fast as possible without warping in order to make it to Death Mountain Summit and deliver the World's Finest Eye Drops to Biggoron. Once delivered, Biggoron is relieved to finally be able to see again. If Link shows him the broken Biggoron's Sword, Biggoron will agree to repair it as repayment for the eye drops. Biggoron remarks that the process will take some time, however, and presents Link with a Claim Check so that he does not forget about it altogether.
Death Mountain Summit
After three days and nights have passed, Biggoron's Sword will be complete. (The waiting process can be shortened by playing the Sun's Song a total of six times.) After that, Link must return and show Biggoron the Claim Check. Biggoron gives Link the strongest sword in the game. (He also lets Link keep the Claim Check, which serves no further purpose. On the N64 version, it's recommended to turn the Check into a Bottle through the use of a glitch.)