Chapter 18: Delos Landing
1. After reaching the interior of the statue with some large gears and a giant chain, take out the empusa and more flyers. Destroy all the eggs afterwards for extra red orbs. Once done, pull the stack of gears and push it to the far right where you can use it as a foothold to reach the upper platform. Destroy the obstacles preventing the giant chain from moving.
Now go back down and use the amulet to restore the chain. Pull the lever all the way to the left then quickly place the stack of gears in between the larger gears so you can use the gear heads to the left as handholds and reach the two red chests and two white chests (if you already collected all Phoenix Feathers and Gorgon Eyes by following this guide, these should contain red orbs only)
Delos Landing Extra Red Orbs/ Collectible chests
Chapter 21: The Forearm of Apollo
1. After getting the Stonemason's Chisel artifact, proceed and step on the circular pressure plate. Leave a copy of yourself again then swing to the next platform. Defeat all enemies, with the help of your new ability then continue to the left. Scale the wall there and make your way to the ledge to the right.
Open the magic/health chest then pull the platform ahead until you can't do so anymore. Leave your copy there but before jumping on that plaform, jump back down to the lower floor. The gate to the left will be open and you can freely loot the red and white chests, as well as destroy the objects inside for some extra orbs.
2. Once you've reached the exterior of the statue, defeat an amazoness, cerberus and wolves. After taking them out, pull the chains on the right and leave your copy to secure it in place. Next, use the amulet to restore the chain enough for the lower part to get connected. Suspend it and use it as a foothold to reach the ledge above. The red and white chests to the right are now restored so you can loot them again. Head inside to the left this time.
Chapter 22: The Ribs of Apollo
After landing on a platform and climbing a ladder, turn to the right first to find two red chests. Continue to the left until you reach another platform where you need to take out more enemies. After clearing the area, look to the left to find a raised ledge with two red chests and two white chests.
Chapter 23: The Furnace
1. From Archimedes' workshop, 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.
Chapter 26: Eyes of Apollo
1. Push the block off the crystal to make it rise and split the beam of light into two. Kill the enemies next. Once clear push the stone block to the left and pull the lever there to lower the beam of light. Don't forget to collect the red orbs to its left. Next, jump to the lower floor and push the stone to the right and use it to reach the ledge. Collect the red orbs to the right then use the ladder to reach two white chests above.
Chapter 28: The Trial of Archimedes
1. As soon as the chapter starts, you'll find the two white chests and a red chest to the upper left.
If you followed this guide, you should be able to fully upgrade your Magic and Health as early as Chapter 18. This section will indicate the location of other white chests in the game. Even if you have fully maxed out your health and magic, finding these chests will allow you to collect considerable number of orbs, allowing your to fully max your magic and weapon upgrades in one playthrough.