He lived with his older brother Walter, who was also a miniaturist, at his studio on Essex Street, Dublin and potentially trained with him also.
From 1769, at age 9, to 1774 Robertson exhibited "designs in hair" at the Society of Artists on William Street, moving on to miniatures from 1775.
In 1814, he became the secretary and later vice-president of the Hibernian Society of Artists, and also served on the committee looking to found an Irish Academy of Painting.
Robertson never signed his works, but they are generally identifiable by his use of pale grey-blue skin tones.
[1][2][3] The National Gallery of Ireland (NGI) hold a number of works by Robertson including portrait of a woman wearing a white dress.