Thanks for the question!
It's great to hear that you have ancestors from County Mayo and are looking to obtain dual Irish Citizenship yourself. I would like to suggest that you have a look at the
Citizens Information page, specifically about this topic. As you can imagine, there are rules and regulations on who is eligible. As your father claimed dual citizenship, and you have grandparents who were also Irish, you may be able to claim under the
Foreign Births Register.
Hopefully, this will be something that you can follow and obtain your dual status.