Question: What act of a mythical hunter-warrior of Irish mythology won him the leadership of the Fianna?

Context articles: Liam Mac an Ultaigh
Cath Gabhra
Hill of Allen
Aillen
Fenian Cycle
Diarmuid Ua Duibhne
Fomorians
Mag Mell
Fionn mac Cumhaill
Goll mac Morna

Liam Mac an Ultaigh of Dublin (fl.
 c. 1965) is an Irish Nationalist and was Chief Scout of the Fianna Éireann from 1965.
 In such tenure, Mac an Ultaigh is most recognized for his work on the Committee that under his administration drafted the Fianna Handbook’s 3rd or 1965 (1st 1913, 2nd 1924) edition, which uniquely of the editions attempts to chronicle the organization’s history.
 Notably, this thorough and well documented Handbook history conclusively disputes traditional histories, which credit the Irish Republican Brotherhood’s Bulmer Hobson with founding the “Scouts” and exposes a, possible, anti-feminist bias in the traditional histories.
 The 3rd Handbook in its section “The History and Tradition of the Fianna Éireann” at its pages 24–26 credits instead the Sinn Féin’s Constance Markievicz or “the Countess Markievicz” with founding “Na Fianna Éireann”.
 As already noted in the Wikipedia article Fianna Éireann, Patrick Pearse has stated that the creation of Fianna Éireann was historically as important to the liberation of Southern and Western Ireland from British rule and the founding of the Irish Free State and, later, the Republic of Ireland as was the creation of the Irish Volunteers in 1913.
 The paramilitary Fianna Éireann youth Scouts were involved particularly with gun running commencing with the 1916 Easter Rising and later in combat, particularly in Dublin, during the Civil War period of 1922-1924.
Cath Gabhra (English: The Battle of Gabhair or Gowra) is a narrative of the Fenian Cycle of Irish mythology.
 It tells of the destruction of the fianna and the deaths of most of its warriors in a battle against the forces of High King Cairbre Lifechair.
 It is notable for depicting the fianna, the heroes of the cycle, in a negative light.
The Hill of Allen ("Cnoc Alúine" in Modern Irish, earlier "Cnoc Almaine"; also Hill of Almu ) is a volcanic hill situated in the west of County Kildare, Ireland, beside the village of Allen.
 According to Irish Mythology it was the seat of the hunter-warrior Fionn mac Cumhaill and the Fianna.
 The site is currently part-owned by Roadstone Dublin Ltd. and extensive quarrying has noticeably changed the profile of the hill.
Aillen or Áillen is a being in Irish mythology.
 Called "the burner", he is a member of the Tuatha Dé Danann who resides in Mag Mell, the underworld.
 According to "The Boyhood Deeds of Fionn", he would burn Tara to the ground every year at Samhain with his fiery breath after lulling all the inhabitants to sleep with his music.
 This only ended with the arrival of Fionn mac Cumhaill, who inhaled the poison from his spear to keep himself awake and slew Aillen.
 The act won him the leadership of the Fianna.
The Fenian Cycle ( ) or the Fiannaíocht (Irish: "an Fhiannaíocht" ), also referred to as the Ossianic Cycle after its narrator Oisín, is a body of prose and verse centring on the exploits of the mythical hero Fionn mac Cumhaill (Old, Middle, Modern Irish: Find, Finn, Fionn) and his warriors the Fianna.
 It is one of the four major cycles of Irish mythology along with the Mythological Cycle, the Ulster Cycle, and the Historical Cycle.
 Put in chronological order, the Fenian cycle is the third cycle, between the Ulster and Historical cycles.
 The cycle also contains stories about other famous Fianna members, including Diarmuid, Caílte, Oisín's son Oscar, and Fionn's enemy, Goll mac Morna.
Diarmuid Ua Duibhne ( ) or Diarmid O'Dyna (also known as Diarmuid of the Love Spot), was the son of Donn and one of the Fianna in the Fenian Cycle of Irish mythology (traditionally set in the 2nd to 4th century).
 He is best known as the lover of Gráinne, the intended wife of Fianna leader Fionn mac Cumhaill in the legend "The Pursuit of Diarmuid and Gráinne".
The Fomorians (Old Irish: Fomoire , Modern Irish: Fomhóraigh ) are a supernatural race in Irish mythology.
 They are often portrayed as hostile and monstrous beings who come from the sea or underground.
 Later, they were portrayed as giants and sea raiders.
 They are enemies of Ireland's first settlers and opponents of the Tuatha Dé Danann, the other supernatural race in Irish mythology.
 However, their relationship with the Tuath Dé is complex and some of their members intermarry and have children.
 The Fomorians have thus been likened to the jötnar of Norse mythology.
In Irish mythology, Mag Mell (modern spelling: Magh Meall, meaning "plain of joy") was a mythical realm achievable through death and/or glory.
 Unlike the underworld in some mythologies, Mag Mell was a pleasurable paradise, identified as either an island far to the west of Ireland or a kingdom beneath the ocean.
 However, Mag Mell was similar to the fields of Elysium in Greek mythology, and like the fields of Elysium, was accessible only to a select few.
 Furthermore, Mag Mell, like the numerous other mystical islands said to be off the coast of Ireland, was never explicitly stated in any surviving mythological account to be an afterlife.
 Rather, it is usually portrayed as a paradisal location populated by deities, which is occasionally visited by some adventurous mortals.
 In its island guise it was visited by various Irish heroes and monks forming the basis of the Adventure Myth or "echtrae" as defined by Myles Dillon in his book "Early Irish Literature".
 This otherworld is a place where sickness and death do not exist.
 It is a place of eternal youth and beauty.
 Here, music, strength, life and all pleasurable pursuits come together in a single place.
 Here happiness lasts forever, no one wants for food or drink.
 It is the Irish equivalent of the Greek Elysium or the Valhalla of the Norse.
Fionn mac Cumhaill ( ; ] ; Old Irish: " and Middle Irish Find or Finn, mac Cumail" or "Umaill" ), sometimes transcribed in English as MacCool or MacCoul, was a mythical hunter-warrior of Irish mythology, occurring also in the mythologies of Scotland and the Isle of Man.
 The stories of Fionn and his followers the Fianna, form the Fenian Cycle ("an Fhiannaíocht"), much of it narrated in the voice of Fionn's son, the poet Oisín.
Goll mac Morna (or Goal mac Morn) was a member of the fianna and an uneasy ally of Fionn mac Cumhail in the Fenian Cycle of Irish mythology.
 He had killed Fionn's father, Cumhal, and taken over the leadership of the fianna, but when Fionn grew up and proved his worth Goll willingly stepped aside in his favour.