Pretty much what has been said here.
-No upgrades, no fairies/potions. Do not get Water Bombs AFTER the Lakebed Temple and do not get Bombchus.
-If you haven't already, equip your wooden shield and find a way to burn it. (The enemies in the Goron Mines are good for that.)
-Use the Ordon Sword if you don't do glitches; if you do, as others mentioned, try out the Wooden Sword glitch.
Things that, surprising, haven't been mentioned.
-Keep the Iron Boots equipped at all times.
-Wear the Magic Armor at all times WITHOUT any rupees. It hinders your movement greatly. (Do not get wallet upgrades past the 600 rupee upgrade needed to get the Magic Armor. Try not to open unnecessary chests.)
The Iron Boots might be a better choice, seeing as the Magic Armor requires you to get the first Wallet upgrade. Perhaps you could try wearing both the Iron Boots and the Magic Armor, but I don't know if it makes much of a difference.
Good luck, and have fun!