How do you find the boss key in Hyrule Castle?

Part way through the castle you will have a choice of going left or right down trails, these lead to a bridge where you fight shield dragons, you reward is the boss key.

After making it to the second floor of the castle, in the main room, there is a choice of two doors, one leading east and one leading west. No matter what path you take, you will end up on a balcony. Go east and enter an ambush. You will kick their butts with your hands tied behind your back...sort of literally. Get the small key and then head west and you will find the big key. I think that's it. I've completed the game so i'm not sure whether or not the directions are correct. It's been a while since i've done this part. Hope I helped!

Once you enter Hyrule Castle and use your Clawshots on the chandeliers, you'll come across a room where you need to light a couple Torches with the Lantern and put out one with your Gale Boomerang. After that, the room splits - to the East and to the West, either way you'll fight a couple guys and then go outside - head to the middle and you'll catch a break...