To avoid paying tax or penalties to the US in addition to tax paid in Ireland, a minimum of 4 forms are required for the US: Form 1040 or 1040A, Form 2555 or 1116, Schedule B, and Form 8965.
If the sole bank account held $10,000 on any 1 day, an FBAR, FinCEN 114, is required. If the sole account held $200,000 on any one day, a Form 8938, FATCA, may be required.