Clais, you can lose your accent if you want to. It's entirely up to you. :)
You're already in a good place, ie. an English-speaking country, and if you end up swapping your Italian accent for an Irish accent, that would still be very charming.
You do need a guide! Someone needs to tell you (nicely) exactly what parts of your speech show that you're a foreigner, and help you practice sounding more local. Don't do this alone. Find someone who will let you copy (even mock) their accent. Do any of your Irish friends have an accent that you particularly like?
I suspect your rhythm, intonation and R sounds are still very Italian, so you can have a close look at those first. Your Italian vowels might be getting in the way of the (Hiberno-)English vowels, too.
If you record yourself with a short text and post it in Discussions, other italki members would be able to give you feedback. Vocaroo.com or clyp.it are useful sites for quick recording.