@gwac,
For mythical heroes look up Fergus, Cu Culainn, Maeve and the
Táin Bó Cúailnge--which means Cooley's cattle raid, and which can reasonably be described as the most important of the ancient Irish legendary cycles. (Maeve's name is also spelled Medb or Mab.)
For "political activists" there's at least one per pub througout the history of the "troubles," and probably a good deal more. Probably the giant of Irish political activists would be Daniel O'Connell, also known as the Liberator or the Great Emancipist, because he accomplished Catholic emancipation. (Prior to his eventually successful campaign, Catholics could not sit in Parliament or hold any public office of any kind, including in the army or navy.) For the rest of it, there is such a welter of individuals in the constant struggle for independence and the civil war after 1921, that it would take a long page to list them all. A period of interest would be the uprising of 1798, for which you should look up Wolfe Tone and the United Irish--a rebellion by both Catholic and Protestant (in fact, the leadership were most Protestant). It would be reasonable to say that Daniel O'Connell was a product of the failed rebellion of Wolfe Tone and the United Irish.
For literature, jeeze, you'd need an even longer list. Just to hit some high spots--John Millington Synge, whose play
The Playboy of the Western World lead to rioting; William Butler Yeats and Lady Gregory of the so-called Irish literary revival (she wrote collections of Irish folklore and mythology which are probably the most accessible to the modern reader). Of course, no such list is complete without mentioning James Joyce and Samuel Beckett (Beckett's most famous play, the English title of which is
Waiting for Godot, was written in French).
In music, people speak highly of Herbert Hamilton Harty--Ravel always complained that he would be remembered for
Bolero, which was not his best nor his most serious work. The same thing happened to Harty, who was famous both as a composer and a conductor--and especially as a interpreter of the works of the French composer Berlioz. But Harty is only remembered these days for a brief work, now a song, which he entitled "Londonderry Air" (air as in a song), which is now known as "Danny Boy." The other truly great Irish composer is Turlough O'Carolan, who lived in the late 17th and early 18th century. Most observers see him as Ireland's great national composer. He composed on the harp, and he composed elaborate Baroque scores based on Irish traditional music.
That ought to get you started.