I can only speak from my own experience on this, so ...
First off I'm not familiar with the term "advanced TEFL cert", but .. I am Irish and have worked in EFL teaching there for the last 3 years. Obviously Dublin is the place with by far the most work in basically every field and frankly I'm not sure how much EFL work exists on a year round basis outside the capital
I would divide the Dublin market into 2 poles : legitimate serious opertaions, and complete cowboys. I have worked for both
serious operations (who pay well eg 20 Euro per hour) will require an ACELS (full time EFL course) cert or international equivalent which in Ireland can only be obtained via having a BA degree. However your ACELS equivalent may be this advanced cert so this might be OK
suffice to say the one good company I worked for required a copy of my degree quialifications for the purposes of EQUALS inspections (European body that inspects language schools)
the 2 slightly less professional schools did not but 100% needed proof of a full time TEFL course completion (again what we call ACELS)
I do know of schools that take university educated people with no ESL qualifications - so the reverse I'm sure is also true
the quantity of work is also seasonal - in summer there is vast amounts, in winter there is significantly less.
The one plus in Ireland is that salaires are relatively high with extremely low taxes on the potential earnings of a EFL teacher