Chapter 2: Sagittarius Bow
On the staircase before you meet Magnus, there is a tapestry. It is actually a hidden doorway that leads to the Zodiac chamber.
Chapter 4: Taurus Arm
In the multileveled room with acid pits, go down the pit that is not full of acid or spikes. You'll find a Zodiac Chamber there.
Chapter 6: Gemini Orbitars
After beating Dark Pit underground, head into the corner. There is a passageway to a Zodiac chamber. This is a randomized chapter, so it might be necessary to do it multiple times before reaching the underground section.
Chapter 8: Cancer Claws
In the room full of constellations, there is a door on the other side of the room. Go along the walkway, but don't step on the jump pad. Instead, go all the way to the other end and drop down to reach the door. It leads to the chamber.
Chapter 10: Leo Cannon
After seeing a Guttler for the first time, head down the path to the far left. It should be in plain sight.
Chapter 12: Virgo Palm
Chapter 14
Chapter 16: Scorpio Staff
In the shaft going down after you get the Aether Ring, the Zodiac Chamber is midway down and to the side.
Chapter 18
After seeing the Souflee in the hot spring, head down the passage left. There is a door behind the building, and inside is the Zodiac Chamber
Chapter 20: Capricorn Club
In the prison, the Zodiac chamber should be on the middle cell to the left. Step on the switch next to the cell to the right to unlock that cell. The back of the cell is actually a hidden passageway to the Zodiac chamber.
Chapter 23: Aquarius Blade
When possible, go backwards on a grind rail. You'll be brought straight to the chamber.
Chapter 24
After going up the first elevator, head down the long path in the opposite direction of where the arrow is pointing. The last Zodiac item will be there.