How to get Biggoron's Sword:

By far the hardest sword to obtain in the game, but indeed the most powerful, Biggoron's sword's fetch quest is the most frustrating thing I have ever done in a Zelda game. Here is a guide to make sure you don't suffer the same agony as I do: 

1. Make sure you are Adult Link, make sure you have thawed King Zora in Zora's domain, and make sure you have Epona. It's also recommended that you familiarize yourself with your territory as well. Go to Kakariko Village when you're ready. It's also suggested that you have the Sun's Song, as you will have to wait three days at a certain point.
   
   
2. 2
   Go talk to the Cucco Lady. She will give you a Pocket Egg. Play the Sun's Song, or wait one day. You will have a Pocket Cucco.
3. 3
   Take the Pocket Cucco, and find the house in Kakariko Village where Talon is sleeping. Use the Pocket Cucco to wake him up. Bring the Pocket Cucco back to the Cucco Lady. She will be happy and she'll give you her brother's Cucco, Cojiro, which she requests to have delivered to him.
4. 4
   Go into the Lost Woods, and from the entrance, turn left.(This is the room where you sell the Skull Mask to the Skull Kid as Child Link.) You'll see a strange-looking blue man sitting against the stump where the Skull Kid was. Give Cojiro to him, he'll be happy, and he'll give an Odd Mushroom to you, and tell you to deliver it to the potion hag in Kakariko Village. Now, the mushroom will spoil, so you're given three minutes to rush to Kakariko Village. The hag is behind the normal potion shop.
5. 5
   Give the Odd Mushroom to the hag, and she'll make you an Odd Potion. Take it back to the Lost Woods, no hurry, you're not timed. When you reach the place where the man was, you'll find instead, a small Kokiri girl who says the Odd Potion is made out of forest mushrooms, and demands you to give it back. She gives you a Poacher's Saw in return.
6. 6
   Head to Gerudo Valley. The bridge is down. No problem. Either Longshot across, or, if you don't have that, use Epona to jump across. Go into the carpenters' tent, and talk to the boss. He excitedly takes the Poacher's Saw and gives you a Broken Goron's Sword in return.
7. 7
   Use the Bolero of fire and go to the top of death mountain, go to the right side of the cliff. A giant goron(Biggoron) should greet you, but he's rubbing his eyes in pain. After talking to you, he says he'll fix the Broken Goron's Sword, but only if you get him eyedrops in return. He hands you an Eyedrop Prescription.
8. 8
   Go to Zora's Domain and present the Eyedrop Prescription to King Zora. He says he doesn't have the eyedrops, but he does have the ingredients. He gives you an Eyeball Frog. You need to get to Lake Hylia to give the Eyeball Frog to the lakeside scientist. And hurry, because you have three minutes before the stuff spoils.DON'T use serenade of water! That will cause the Eyeball Frog to spoil.
9. 9
   Once at the Lakeside Laboratory, give the scientist the Eyeball Frog. He's excited at first because he thinks he gets to eat the frog, but he becomes discouraged as he makes the eye drops for you. He gives you Biggoron's Eyedrops, and they spoil in four minutes, so you need to get yourself from Lake Hylia to the top of Death Mountain. Quickly. DON'T use Bolero of fire! It will cause the eye drops to spoil. If you go through Darunia's room in Goron City time will stop as you pass through the crater and you can pop out at the big goron.
10. 10
    Once you give the eyedrops to Biggoron, his mood greatly improves, and he promises to make you a sword in three days. He gives you a Claim Check, and you can either wait three days, or play the Sun's Song six times.