Open the two white chests and a red chest to the upper left then head to the right and open the door. Once the eyes' enclosure is open, go there and pick it up to be added to your inventory.
After the platform descends, use the Eye on the illusion then grapple it to enable the platform to rise up again. The platform will stop and you have to defeat several enemies. These enemies drop magic orbs upon death and they're dangerous enough to quickly decimate you if you give them the chance to corner you. Use your magic attacks. At this point, you should have already a fully upgraded element or two. You should do your best to minimize your damage at this point; otherwise, you'll have a grave situation in the next waves. Abuse your spells as necessary. It will help if you collected all Phoenix Feathers and Gorgon Eyes at this point, which will make this challenge manageable.
Do the same thing again to release the clamp holding down the platform. It will stop again and you'll have to fend off a series of enemy attacks again. You'll have to kill amazonesses and their harpies. After taking them out, the columns will start spewing fire in intervals as you deal with enemies. You can roll towards the fire to avoid getting burned and to escape the enemies in this narrow death trap. After all enemies are taken out, destroy the fury's illusion and grapple the clamp to make the platform ascend again.
The platform will ascend again only to stop for the third time. Again, if you didn't manage to keep your HP up in the last wave, this wave could spell trouble for you. Defeat the centaur by blocking its simple attacks and evading its charges. Use your fully upgraded element's strong attack (Soul of Hades is a good example) to deal extra damage at a safe distance. After taking out the centaur, your HP will be recovered a bit. Next, the shades. Your shadow will be a great help in throwing these light enemies airborne. It will be safer there so perform air combos often. These enemies drop magic orbs so use your magic to soften them up and allow you to weaken them for execution faster. After clearing all enemies, release the last clamp to complete the trials.
Once you've reached the previous floor, head to the right and close the door. Go the enclosure and destroy the illusion on the handle bar and pull it until the mirrors inside the enclosure align. Leave your shadow there then head to the illusion gate. Destroy it using the Eyes then go past the portal.
After the scene, wait for the floor to stop then head to the right of the enclosure to find the last treasure of the game. Open the door for a scene.
Trial of Archimedes Treasure