are you a U.S. Person in any way, are you a citizen or entitled to hold a U.S.passport? If not then you can provide a W8-BEN form to the administrator of your shares and they should not then withhold any U.S. tax. The form can be downloaded from the IRS website, you print it, sign it and provide it to the admin. You may need to provide back-up docs like passport copy or proof of address, or you may have provided these already for anti money-laundering.
You don't need to provide the form to the IRS at all, just the admin.
For the tax already paid, I doubt you can get that back through Irish revenue, I would chase the admin for this, you can sign the W8 retrospectively and they should (although I haven't done this bit before myself) be able to claim it back for you.