Note: I am not a dataminer. This guide is incomplete and there may be missing information like missing resonating crystal locations. This is by no means a high-quality guide. Note that these are just the possible locations and this only serves as a guide on where to look for the crystals. A single expedition will not have every single crystal present.

TLDR
Break 4 small crystal to break the giant crystal in the middle of the map. The buff you get from inside the giant crystal prevents you from receiving a debuff that you encounter from the 2 forts located on the east and west sides of the map.

Please note, I have added two resonating crystals that appear on the lower level map to the upper level map as I believe they fit better there. If you overlay the two maps together, some crystals may overlap, that's the reason.

The Favor of the Great Hollow
In the Great Hollow, there is a buff you can receive upon shattering the great crystal located around the center of the map. The description of the buff, the Favor of the Great Hollow, reads:
"Breaks Crystal Curse, and when Sacred Flasks are exhausted, boosts art gauge."

About the Curse
The Crystal Curse is a miasma that eats away at life, exuding from the crystal founds in the Great Hollow. In-game, the Crystal Curse is a debuff that cuts your health by 50%. You will encounter the Crystal Curse upon entering either of the two forts located at the east and west of the map.

What are Resonating Crystals?
In-game description:
"Crystals found in the Great Hollow, part of the root system of the giant crystals. Their resonance is said to cause giant crystals to shatter."

Why Does This Matter?
The buff you receive from the great crystal, the Favor of the Great Hollow, neutralizes the effects of the Crystal Curse, allowing you to explore the two forts on either side of the map at full health.

If entering in from the northern part of the map, keep your eyes open for this crystal when moving towards the center of the map.


Here's a weird one that does not show up on the surface layer but rather the underground layer, you find this one hugging the cliffside.


When traversing the area around the merchant by the broken bridge, check beside the bridge on the lower level.


If you're nearby the merchant by the broken bridge, there's this one you can look out for, but it's annoying to go out of your way to get to. The upper level of the central section has these crystals you can climb at the west for a potential resonating crystal. If there isn't one there, well, you just wasted some valuable time you could have spent fighting trash mobs instead.


When entering the map from the south, be sure to check the peak of the western ruins for a potential crystal. Use the spiritspring at the south of the POI for a quick shortcut here. There may be some small mobs surrounding the crystal here.


At the crossroads at the northeast, there's various paths you can take. West towards the main central area, take the spiritsprings up to the mines, spectral hawk south towards the underground ruins and dupe church, or take the slopes down to the lower area by foot. Several resonating crystals you can get around this area.