From the start, follow the passage out to the first open area. Go to the cave to the south, and at the first fork take the righthand path. Keep following this passage round, past the area to the right (with Brown Chaos Serpents) until you reach a left junction with what looks like a dead end. This is a rotating door, which rotates clockwise when activated. Go through here and climb the steps to a new area, then head to the landbridge over lava to the east. At the end of the bridge the Horn key can be found, which is used to access puzzle switches on Darkmere and the Caves of Circe.
First puzzle switch
This puzzle switch requires the Cave key, which can be found on the Caves of Circe. From the start of the map, head south. Keep heading south until you reach an open, fairly dark area with a large number of Brown Chaos Serpents. Use the Cave Key to unlock the portal and the teleporter. Step in the teleporter, which will lead you to the centre of the map in a lava area, where you will be surrounded by Afrits. Kill all the Afrits and a magic staircase will appear allowing you to reach the raised platform. Go inside the large V shape and find a Mystic Urn and the first puzzle switch.
Second puzzle switch
This puzzle switch requires the Swamp key, which can be found on the Darkmere. From the first open area at the start, head north until you reach a tall, grey passage. Stick to the outside of this passage, and follow it as far as it will go. One of the inside walls should lower down, revealing a large slime lake populated by Stalkers. Beyond this lake there are some steps leading up to the Swamp Key door. Go inside and activate the switch. This will lower a large wall north-west of your position, revealing a large temple like structure. Fight your way inside the structure and you will see a portal (which leads to Darkmere). Behind this portal you will find the second puzzle switch.