In order to create the Iridescent High-Purity Mucus, you will need a Fairystone Fragment.
This is a fairly straightforward synthesis, requiring only two ingredients. You will automatically obtain one of them at the start of the chapter.
You will also learn the recipe automatically once you return to the Atelier.
Collecting the Fairystone Fragment
You can easily find Fairystone Fragments just outside the Cleria Region Atelier.
First, head across the wooden bridge north of the Atelier.
Past the bridge, walk a short distance east until you reach a big boulder. Collect the crystals on the ground to obtain a Fairystone Fragment.
This is the only additional ingredient you will need for this synthesis.
Synthesizing the Iridescent High-Purity Mucus
With all ingredients in hand, return to the Cleria Region Atelier. Select the Iridescent High-Purity Mucus recipe.
Start by adding the Iridescent Mucus in the Effect 1 loop. Federica will automatically give you the Iridescent Mucus at the start of the chapter.
Next, move to the Effect 2 loop on the top and add a Fairystone Fragment.
Synthesize the recipe straight away in order to save ingredients. This quest does not have a minimum Quality requirement.
Fast travel back to Sardonica – Artisans’ Union Headquarters. Deliver the Iridescent High-Purity Mucus to Federica in order to advance the main story. Federica will then join your party.