Vessel of Mediocrity (Part 2) is an Adventure Mission that uncovers more secrets behind the tragedy that befell Cyrille, a Mysterious Child who you first meet in the Backwater Pass. While she remains a ghost of Belobog's dark history, the second installment of her Mission will shed more light on what transpired once upon a time. I thought that the puzzles in this quest were a little trickier than the first, but I broke down all the steps below to walk you through how to complete them from start to end.
How to unlock Vessel of Mediocrity (Part 2) Mission in Honkai Star Rail
To unlock Vessel of Mediocrity (Part 2), you must first complete the prerequisite Mission, Vessel of Mediocrity (Part 1). Once that's done, head to the Silvermane Guard Restricted Zone.
If you completed the prerequisite, you'll find a Mission icon on the left of the area. Head there to find a Mysterious Woman, who you must speak with to initiate Vessel of Mediocrity (Part 2).
All The Fool's Box puzzle solutions in Vessel of Mediocrity (Part 2) – Honkai Star Rail
The Fool's Box puzzle solution #1
Upon starting the puzzle, push the box above two times so that it's leaning against the northern box.
Next, push the box above two times so that it's at the rightmost part of the grid.
You then need to push the box above once. It should move one step upward.
Once that's done, push the box above once so that it moves rightward. Doing so will allow you to reach the child on the left. Rescue the child to complete this segment.
To free the second child, start by pushing the box above once. It should move upward.
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Next, push the box on the bottom right once. It will move upward, giving you access to the last box blocking the child.
Lastly, push the box above once so that it moves to the left, finally unblocking the second child. Interact with the child to Rescue her, completing the puzzle.
You'll be rewarded with a Bountiful Treasure—don't forget to loot it! Once that's done, speak to the Mysterious Woman to proceed with the second puzzle.
The Fool's Box puzzle solution #2
Upon starting the second puzzle, you first need to push the box above three times until it hits the rightmost edge of the grid.
Next, push the box above once so that it moves upward, hitting the box above it. This will completely unblock the nearby child.
Then, push the box blocking the bottom child once. This will move the box downward, also opening up a path for the child beside it.
If you've followed all the steps, the middle and right children should be unblocked, as pictured above. You need Rescue both children by interacting with them before proceeding, as the puzzle can't be solved without getting them out of the way.
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Once that's done, you'll be able to access the box pictured above. Push it once so that it's on the leftmost edge, allowing you to reach the final child. Rescue the child to complete the puzzle.
You'll be rewarded with a Bountiful Treasure. Loot it, then speak to the Mysterious Woman. After that, head to the southern Space Anchor (still within the Silvermane Guard Restricted Zone) and speak to Dunn nearby.
Dunn's Text Message
After completing all of the above, wait until the server reset to get a text message from Dunn, pictured above. Respond to it, then meet Dunn at the Silvermane Guard Restricted Zone to complete the Adventure Mission. You can then proceed to the final Mission in the quest chain: Vessel of Mediocrity (Part 3).
For more HSR guides, check out Honkai Star Rail Simulated Universe World 3 Guide: How to beat Gepard here on Pro Game Guides.