In order to synthesize the Glass Goblet, you will need Stained Flowers.

Here are the requirements you need to meet before proceeding:

1. Collect Stained Flowers: This is one of the mandatory core ingredients for the Glass Goblet. You can easily find Stained Flowers near the Cleria Region Atelier.
2. Gather Ashen Sand: You will also need to synthesize Polishing Powder, which requires Ashen Sand.
3. Synthesize Polishing Powder: As mentioned above, Polishing Powder is another mandatory core ingredient for the Glass Goblet.

You will automatically learn the recipe once you enter the Atelier.

Collecting the Ingredients

First, you will need to obtain the Stained Flower for the Glass Goblet. You will also need Ashen Sand for the Polishing Powder recipe.

Stained Flower Location

You can easily find Stained Flowers near the Cleria Region Atelier. 

Head across the wooden bridge north of the Atelier. Next, follow the dirt trail up the hill to the west.

Use the staff on the flowers in order to obtain a Stained Flower.

Ashen Sand

You can easily find Ashen Sand in Sardonica as well. Use any of your tools on the barrels around the city in order to collect Ashen Sand.

Synthesizing the Glass Goblet

After obtaining all ingredients, return to the Cleria Region Atelier.

Start by synthesizing the Polishing Powder.

Next, select the Glass Goblet recipe.

Start by adding a Stained Flower to the Effect 1 loop.

Insert a Magical-category ingredient in the Effect 3 loop. You can use a Stained Flower again.

Insert Polishing Powder in the Effect 2 loop to fill out all core loops.

You can now synthesize the recipe, since there is no Quality requirement.

After creating the Glass Goblet, fast travel back to Sardonica – Artisans’ Union Headquarters. Deliver the Glass Goblet along with the Fairystone Pendant to Alberta in order to complete the quest.