Where do the different Irish accents comes from?

Well, as far as the Irish language goes (or any indigenous language to an area for that matter), it must have always had different dialects from time immemorial as in the past, travelling to different areas was much harder than it is now so different dialects also develop. Then when the brits came to Ireland, people who were speaking different Irish dialects must have influenced their english differently according to their dialect.

Secondly, people from different parts of England must have settled different areas in Ireland and brought their own dialects with them.

Thirdly, and in the context of Dublin most importantly, social class is a very big influence to dialect. People in South dublin who are generally more affluent must have been way more influenced by posher and higher-class English dialects than working class people in North Dublin. It could have also been that people in working class areas in north Dublin switched from Irish to English later than upper class people in South Dublin.

Where I am from in the Netherlands, every province has its own traditional dialect, some of which (like the one I speak aside from standard Dutch) are hardly intelligible for people who only speak Standard Dutch. And within the provinces you can often hear which village people are from based on the dialect.