Credit cards are accepted in most places in Ireland. Some smaller shops and some restaurants don't accept them. Others will place a minimum purchase amount before allowing you to use a card. But it is always good to have cash to cover your purchase in case their card machine decides to stop working. I have never been charged any additional fees for using credit card anywhere in either part of Ireland. I never use a debit card for purchases anywhere, so can't answer on that.
What foreign transaction and conversion fees does your favorite credit card charge? Many are available that charge nothing.
Probably too late now, but you could open an account at a bank that isn't so fee hungry and use it when you travel out of the country. Capital One 360 account charges no fees for any ATM transactions done anywhere. No looking for an affiliate, just pick an ATM that you like and use it. (If the ATM owner charges you a fee, you do pay that. But not many ATMs in Europe charge a fe so far.)
One thing to think about is what is less stressful to you: carrying enough cash with you to cover expenses for 2 weeks or paying the fees at ATMs. Also, you will need to bring Euro for Ireland and Pounds for Northern Ireland, if going to both places. Banks in Ireland don't do currency exchange for anyone not having an account with them. You would have to find a currency exchange if you are bringing US$, and they charge way more than BofA does for ATM transactions.
If you get your Euros and Pounds from your BofA location before leaving the US, they will charge a marked up exchange rate which may still be more than what the fees are for the ATM withdrawal. The bank will tell you it is a great rate, but do the math. How much will they charge you for €1000 if you get the cash at the branch today? How much will €1000 cost from an ATM in Ireland today? Include all fees for both options. This should help you decide.
And whatever option you choose, notify your credit card issuer as well as your bank for your debit card where and when you will be in Ireland so they don't cut you off for suspected fraud. And remember the Northern Ireland is a separate country from the Republic of Ireland.