* Intellectual brilliance: λάμπρος (lámbros) meaning "shining," "bright," could be used, or perhaps φυής (phuḗs) meaning "nature," could be used in the sense of a naturally brilliant mind. You might even use a phrase like ὀξύνοια (oxýnoia) meaning "sharpness of mind."
* Brilliance of a gem or light: λαμπρότης (lamprótēs) is a good choice, meaning "brightness," "splendor." ἄστρον (ástron), meaning "star," could also work metaphorically.
* Brilliance of performance or achievement: ἀρετή (aretḗ) meaning "excellence," "virtue," might be most appropriate, depending on the nature of the brilliant achievement.
Therefore, the best Greek word for "brilliance" needs to be chosen based on the specific context in which the word is used.