Betagh was descended from a branch of an old Roman catholic family in Meath, Ireland, which, through the Cromwellian confiscations, lost considerable estates.
He spent most of his Jesuit years of spiritual and intellectual formation in France and was ordained a priest at Pont-à-Mousson on 24 May 1766.
In Dublin he worked with Fathers Austin, James Mulcaile SJ, and Fullham in the old chapel at Rosemary Lane, and taught at the school in Saul's Court.
Betagh established free schools in Schoolhouse Lane, off Cook Street, then in Skinner's Row, and finally in Smock Alley, catering for about 330 boys.
Amongst his pupils were the future Archbishop of Dublin Daniel Murray, and the founder of Clongowes Wood Fr.
Until just before his death he taught each evening at these schools and provided clothing for the most destitute of the pupils, where a total of over three thousand boys had been educated.
The chapel in Rosemary Lane was in a ruinous state, but before Betagh died the foundation-stone of the new Church of SS.