1: To get the biggoron sword you first have to go to Kikoriko Village. Go to the chicken lady and she will give you an egg. Hatch it and go to one of the houses with Talon in it. Wake him up and go back to the chicken lady and she will give you a blue chicken named Cojiro.
2: Go to the Lost Woods and after entering go to your left and show the man Cojiro. He will give you the odd mushroom.
3: Take the odd mushroom to the weird potion lady in Kikoriko Village. She will give Link odd potion.
4: Take the odd potion back to the Lost Woods. This time the man won't be there but a little girl. Show her the odd potion and she will give you the pacher's saw.
5: Then go to the boss of the carpenters who is in Gerudo Valley and give him the poacher's saw. He will give you the broken goron tool.
6: Go to Death Mountain and show the broken goron tool to the huge goron that stays in front of Death Mountain Crater. He can't fix it because his eyes are itching. He will then give you a prescription.
7: Take the prescription to Zora's Domain and give it to King Zora and he will give you an eyeball frog.
8: Then take the eyeball frog to the Lake Hylia lab. Give it to the professor and he will give you the eye drops.
9: Take the eye drops back to the big goron and he will give you a claim check. Then take out your ocarina and play the Sun's Song about 6 to 8 times then talk to the biggoron and he will give you the biggoron sword.
Note: If you have time in any shipments don't warp yourself to the place because once you warp somewhere the time will become 0:01 and you will then fail the shipment and will have to do the last step over again.