The Cottonian Chronicle for the year 1022 notes:

Leuuelin filius Seisill rex Venedocie pugnauit contra Reyn, qui se dicebat esse filium Maredut; et deuictus est Reyn in Ostilo Guili[.source] (Gough-Cooper, c345.1).

Translation: King Llywelyn ap Seisyll of Gwynedd attacked Rhain, who said he was a son of Maredudd; and Rhain was totally defeated in the scorching of Abergwili (Remfry, 209).

The Peniarth 20 version of Brut y Tywysogion provides further details about the battle:

Translation: And after there had been great slaughter on either side equally, with the men of Gwynedd fighting steadily, Rhain the Irishman, and his host were defeated.? And the men of Gwynedd pursuing them cruelly vengeful, slaughtered them and ravaged the whole land, and carried off all the chattels. And he himself was never seen again. That battle was at the mouth of the river Gwili, at Abergwili (Jones, 12).

The Red Book version and Brenhinedd y Saesson of Brut y Tywysogion give slightly differing accounts, but the location is the same in all sources. The identity of Rhain is uncertain (Thornton). Llywelyn ap Seisyll was the king of Gwynedd and died in 1023 (Charles-Edwards, 556?7).

The battle can likely be located to the meadows around the confluence of the Gwili and the Tywi, south west of Abergwili (SN 432 204).

RCAHMW (Battlefields Inventory), Dec 2016

Bibliography
Charles-Edwards, T. M., Wales and the Britons 350?1064 (Oxford University Press, 2013).
Gough-Cooper, Henry (ed.) The Cottonian Chronicle: Annales Cambriae, The C Text from London, British Library, Cotton MS Domitian A. i, ff. 138r?155r, online edition.
Jones, Thomas (gol.), Brut y Tywysogyon: Peniarth MS. 20 (Caerdydd, Gwasg Prifysgol, Cymru, 1941).
Jones, Thomas (trans.), Brut y Tywysogyon or The Chronicle of the Princes Peniarth MS. 20 Version (Cardiff, University of Wales Press, 1952).
Thornton, David E., `Who was Rhain the Irishman??, Studia Celtica, 34 (2000), 131-49.