In order to unlock The Riddle Quest you must obtain 10 Medallions of Courage in the Four Swords (after each level in the Four Swords you will obtain a Medallion of Courage). After this, go to the Lumberjack's House in A Link to the Past and talk the the lumberjack to start the riddle quest. He will hand you a basket and now you have to obtain 10 different items. Use your bug catching net to get an item and put it in your basket. After each item you collect bring to the Lumberjack to get the clue for the next item. Once you complete The Riddle Quest you will learn a new sword technique called The Hurrican Spin.
Riddle Quest Question #1
Riddle: "Cock-a-doodle-doo!"
Answer: A Cucco
This one is pretty simple, all you have to do is go to Kakariko Village and I am pretty sure you can find one on your own.
Riddle Quest Question #2
Riddle: "The scissors by the water..."
Answer: A Sand Crab
You should find a sand crab around the cave east of Lake Hylia where you got the Ice Rod. The path starts below the lake and wraps around to the cave.
Riddle Quest Question #3
Riddle: "It's shiny and red."
Answer: A Red Rupee
A Red Rupee can easily be aquired by cutting down bushes, digging, or hacking at enemies. Or, if you have troubles like I did, go to the Cemetary in the Dark World and ram into the pile of rubble in the north-east corner - as shown in the picture.
Riddle Quest Question #4
Riddle: "It's moist and fresh..."
Answer: A Fish
Fish are found in puddles around Hyrule. The easiest way to get one is go to Swamp Draining pool west of Lake Hylia on the map. Once your inside, drain the puddle and catch the flapping fish left of the drain.
Riddle Quest Question #5
Riddle: "BOOOM! Skitter-scatter... What is it?"
Answer: An Octoballoon
Octoballoons are big floating creatures that explode and split up into eight little monsters. You have to catch one of the fast moving small ones. Travel to point eight using your flute. Or you can use the path to the Ice Cavern east of Lake Hylia to find one.
Riddle Quest Question #6
Riddle: "Sprinkle and watch it wobble..."
Answer: A Slime
This is pretty easy. All you have to do is encouter a hylian soldier then sprinkle some Magic powder on him and he will become a Slime.
Riddle Quest Question #7
Riddle: "It munches on nuts..."
Answer: A Squirrel
The only place you can find a squirrel is the clearing in the Lost Woods where the Master Sword is. Go there and swipe a squirrel.
Riddle Quest Question #8
Riddle: "Pull it out, but... too bad!"
Answer: A Fake Master Sword
Go to the Lost Woods and look around. You should eventually find a fake Master Sword that you can get.
Riddle Quest Question #9
Riddle: "It's red and sweet..."
Answer: An Apple
Some trees in Hyrule have apples that fall when you charge into them with your Pegasus Shoes. The easiest one to find is one screen down from the Lumberjack's House. It is the lone tree in the bottom-right of the screen. Charge into it and get the apple.
Riddle Quest Question #10
Riddle: "A speculated wanderer..."
Answer: A Cukeman
The Cukeman can be found by sprinkling some Magic Powder on a regular Buzzblob. They can be found in the Lost Woods and outside the Witch's Hut. These can shock you so be careful around them.
