First of all, I know 1st, 2nd, and 3rd world countries are outdated terms, but it's the best way I could convey what I was trying to ask.
Ireland's rise to economic success (we'll just ignore the recent recession for now) just seems out of line with that of a former British colony. Especially given that it was a small island with few natural resources to speak of, a long history of oppression by the British, and even after independence, Britain was Ireland's main trading partner.
And when you factor in a population cut in half by the Great Famine and a long tradition of emigration even after independence, it just doesn't make sense - even though I've studied the history books on this topic.
Now, I'm well aware that Ireland didn't become truly prosperous until the 1990's, but the rate at which it climbed to the top tiers of GDP and economic success is still rather startling for a nation not even 100 years old.
Other British Colonies which became independent in the 20th century also became prosperous.
Australia, Bahrain, Canada, Malaysia, New Zealand, Singapore, Oman, Qatar, United Arab Emirates
are all British colonies which became independent in the 20th century and are prosperous today.
(This also assumes that you consider Ireland to be a colony, which it was not, since it was part of the United Kingdom of Great Britain and Ireland since the Acts of Union in 1800.)
You are assuming that Ireland started at a similar economic baseline to other British colonies. This isn't the case. While average income in Ireland was lower than the UK, it was much, much higher than that of the average Imperial subject in India or Africa.