Kill all enemies then operate the gear nearby. Quickly jump on that platform and wait for it to return to its original position. Follow the path until you reach what seems to be a workshop. Head to the left and examine the shining object on the table beside the red chest to get another treasure. (Archimedes' Treatise)
Pull the crank to open up the lid in front then jump through it to reach the furnace below. You'll find two white chests in the area as well. Operate the gear to the right to lower the gate, then move the pile of coal found in the upper right compartment.
Move the coal and place it beside the second gear. Operate the gear to create sparks which will light up the coal and burn it to ashes almost instantly. Now move the coal pile back to its original position and restore it using the amulet. Next, pull the container again and place it inside the compartment beside the first gear. Operate the gear for the molten liquid to fill up the container.
Once the container is filled, take it out and move it to the furnace to the left and place it under the pile of coals. Restore it using the amulet and the fire should reach the coal above, bringing the surface to life. Exit and you'll have to deal with more enemies. Defeat them all then operate the first gear again. Ride the same platform and backtrack to the workshop. Now you have to make it to the upper part of the furnace using the moving lids as footholds.
After getting lifted, carefully cross the walkway where a hanging cauldron is pouring fire on it. After making it to the other side, scale the ledge to the left then climb up to the conveyor belt. Head to the right first to find two red chests. Head to the left this time until you reach a gear. Operate it and before going to the right, make sure you have a full magic meter.
You'll be trapped between two cauldrons and you have to defeat all enemies before you get burned to death. Don't hesitate to use your magic attacks to take control of the enemies. Deploying your copy will also help in controlling the crowd. Once all enemies are defeated, the fire columns will disappear and you can continue forth.