If you are leaving from Rosslare, it is rather difficult to do the west coast in a N-S direction. But since the W coast includes a lot of heading E and W out all those peninsulars, then it probably isn't so important.
You will find in 3-4 weeks you can't go everywhere, and some lovely areas you will have to miss. Donegal is of course wonderful, but it is worth a week, and you haven't got that when you have all the rest of Ireland, so on this occasion it makes sense to give it a miss. Personally I'd probably take the train to Sligo rather than ride it, as the Irish midlands are not so terribly interesting for cycling, though the area is not without interesting places to see on the way. You'll take half a week to get from Dublin to Sligo by bike, and I'd rather have that time in the west, and a bit more freedom to take loops to see interesting little areas throughout the west.
Things not to miss in a trip of that length of time include Achill Island, Connemara, the Aran Islands, the Burren, Dingle, the Ring of Kerry.
You will of course want to ride on little Irish lanes, because it's fun and the traffic on the main roads isn't.You won't be able to travel on a pile of 1:50 000 maps, which is what is needed to follow all the little lanes with 100% accuracy, so sometimes you will have some navigational amusements.
Irish lanes have a large chip size and a lot of patches, which makes for slow going, especially with the breeze. Plan on 50 miles (80km) a day.