After the death of his father Bregor, Bregolas would have become the head of the House of Bëor. He served with the Elf-lords Angrod and Aegnor in the northern land of Dorthonion, and he was by their side when the forces of Angband launched the sudden and devastating attack that would become known as the Dagor Bragollach. Bregolas died quickly in that assault, but his sons survived to join their uncle Barahir. With Dorthonion under Morgoth's control, they became outlaws in the land of their father.
The published Silmarillion only mentions the two sons of Bregor: Bregolas and his brother Barahir. The three daughters shown here appear on the more detailed genealogy of the House of Bëor in volume 11 of The History of Middle-earth.
Most sources (including the text of The Silmarillion) give Bregolas primacy over his brother Barahir, and what dates we have confirm that Bregolas was the elder brother by seven years. The abbreviated genealogy of the House of Bëor in The Silmarillion shows Barahir to the left of Bregolas, but this is presumably a mere question of convenient layout and not meant to show their relative ages.