The owl furnace key is kept with the cat tribe. To acquire it, you need to save the cat Camuria from the rat tribe.

The rat tribe quest can be started by talking to Camuria's father in Naneko town.

Once you acquire the owl bomb, you can break boxes. The rat tribe's crest is visible on the windmill (Bakery) in Rodia.

Once you enter the pantry, you'll see the same crest inside.

Break the wall beside the symbol to reveal a hidden path.

In the next room, you need to break another wall. This one is obvious, as there's light seeping through.

The next room takes you to a door where you need to use the crest to gain access.

You are now inside the dungeon that Camuria is trapped.

Push the crates in this room below to create a path to the door.

Inside, you'll fight the Rat king. Go back to Camuria to free him.

He will be in Maneko's house. Talk to him here to get the cat tribe's symbol.

Back in Naneko town, in the North west, there's a mechanism where you can place the symbol.

Inside you will find the chest that contains the Owl furnace key

The owl furnace is the northernmost dungeon in the game.

You can reach it by following the northern exits in Leon heights. You'll know you're near when you see the lava

• Upon entering, you'll find yourself in a dark corridor. Light up all the lanterns
  
• You will enter the main chamber of the owl furnace
  
  
  Activate the mechanism for lava level control
• You need to light the braziers with symbols in the correct order. The pattern was seen inside the Boko pit. Light the south-eastern one first (Eye), then the north-west (Triangle), then north-west (Broken symbol). The last one is the south-west one, it has a whirpool symbol. Thanks Keheuk for verifying the order
  
• Notice a moveable block in the bottom part of the last brazier. Push this block all the way to the bridge and through a gap
  
• You will have an orb shaped switch at the end of the bridge. Toggle it to let the lava rise.
  
• Once on the other side, enter the top gate to reach the first and the most complex puzzle of this dungeon.
  
  
  The masks
• Push the balls around to match the colors of the masks
  
• The top left door will open, enter it
  
• There are tough enemies here, make sure to dodge and not engage too much. They respawn frequently
  
• Raise the bridge by turning the lever
  
• Go to the other side, and dig at the extreme left to reveal a pressure plate
  
• Place the nearby urn to hold the switch in place
  
• On the bridge, toggle the lever. Go through the opened door. Remember, the door next to this needs a dungeon key.
  
• You will arrive at a corridor with a turret shooting lava. Don't go to the right yet. go through the top-left door. Your objective is to extend the tongues of 4 coloured masks so that you can reach the end of the dungeon. 2 of these are done when the lava is raised, the other two when lowered.
  
  
  Green and Black masks
• You'll reach a room with a switch ahead, toggle it to start a platform. Get on it.
  
• Enter the topmost room
  
• Once you reach the room with the rolling balls, toggle the switch to lower the gates.
  
• Throw a bomb on the level blocked beside the gate. Once past the gate, throw a bomb again to raise it, you'll need it later.
  
• In the next room, go up and into the door above.
  
• Step on the switch to lower a platform to go back into the previous room from an elevated door.
  
• Push the heavy block down, and into the pressure plate
  
• Go back up and into the next room. Avoid the lava, and you'll come across a room with moving balls. Make sure that you have lowered the gate in the previous section, otherwise the last two balls won't be moving.
  
• The next room will have the red mask, but you cannot reach the lever to extent its tongue yet. You have to raise a platform, but the controls are in the next room, filled with lava. We will revisit this room later.
  
• For now, unlock the bottom exit, and exit to the central room with the moving platforms again.
  
• This time, go through the door in the extreme left.
  
• You will get a dungeon key here
  
• Go back to the room with monsters and enter the room that had the lock on it. You can extend masks' tongue here. There's a lever AND a switch, make sure to toggle both.
  
  
  Blue and Red masks
• Time to lower the lava
  
• Go back to the room where you raised the lava, and toggle it to let it lower. Once you toggle, you can die to instantly spawn back to the door near the mask puzzle.
  
• With the lava lowered, go through the top-right door in the mask puzzle room
  
• Push the block down to bridge a gap to another door down below.
  
• Go through the top-left gate and back into the room with monsters, and this time, lower the bridge down.
  
• You can now reach the door below and the next room gives another dungeon key
  
• Go back to the room with moving platforms, and disembark on the bottom right platform. You will see stairs that lead to a door with a lock
  
• Go through this maze and you will eventually reach a room with a lever.
  
• Raise the platforms just enough so that you will be able to reach another lever by going through the next room
  
• Back out, in the moving platforms room, get to the second platform and get to the central tower.
  
• This room will allow for a masks' tongue to be extended
  
• Raise the lava again
  
• Go to the room in the top right area of the moving platforms room
  
• You can now extend the final tongue, the Red one's.
  
  
  The triangle owl key
• Before going to the end, you need the triangle owl key
  
• The triangle owl key is beside the lava raising mechanism. Go back to that room and stand on the lone tile that you pushed at the beginning. Lowering the lava you will reach a switch that spawns the red chest
  
  
  Boss and Orb
• Go to the corridor room (the one with the turret) and go to the extreme right. You can reach the end as all tongues are extended
  
• Use the owl key to start the boss fight
  
• You will get the red orb, one of the three needed to end the game