Only [Legendary+] gear can be advanced.
Use the required materials to advance gear to Primeval R1 or Primeval R2. Currently, the highest possible quality is Primeval R2.
Materials necessary to advance gear to Primeval R1 can be purchased from the Dusklight Emporium after clearing Main Story Chapter 18 or can be obtained offline after clearing Main Story Chapter 22. Materials that can advance gear to Primeval R2 can be purchased from the Dusklight Emporium after clearing Main Story Chapter 23 or can be obtained offline after clearing Main Story Chapter 28.
Materials necessary to advance gear to Primeval R1 can be purchased from the Dusklight Emporium after clearing Main Story Chapter 18 or can be obtained offline after clearing Main Story Chapter 22. Materials that can advance gear to Primeval R2 can be purchased from the Dusklight Emporium after clearing Main Story Chapter 23 or can be obtained offline after clearing Main Story Chapter 28.