To get Biggoron's Sword, you must go through a trading game, like Zelda: Link's Awakening for Game Boy. I will give the code in step-by-step order:
2. Go to the Lost Woods and you will see a boy on a tree stump. Seeing the cucco will lift his spirits and he will give you an Odd Mushroom to deliver to his grandmother in Kakariko Village.
3. The woman in the potion ship will give Link an Odd Potion in return for the Odd Mushroom. Bring it back to the Lost Woods.
4. When you get back to the Lost Woods, the boy will be gone and a young girl will be in his place. Give her the potion in return for the Poacher'sSaw.
5. Go to the carpenter in Gerudo Valley. Give him the Saw and he will give you the Broken Goron's Sword.
6. Make your way up Death Valley and visit Biggoron. He will take the sword and give you a prescription for eyedrops from King Zora.
7. Go to Zora's Domain and bring him the prescription. He will give you an Eyeball Frog, the main for the potion. Bring the Frog to Lake Hylia.
8. Bring the Frog to the Professor at Lake Hylia. He will turn the Frog into the eyedrops.
9. Quickly get back to Death Mountain and give the eyedrops to Biggoron. He will give Link a Claim Check for the sword.
10. Wait 3 days and return to Biggoron. Give him the Claim Check and he will give you Biggoron's' Sword.
Biggoron's Sword is the most powerful weapon in the game. It is twice
as strong as the Master Sword! However, it is so huge, that you cannot use
the sword and the shield at the same time.