His brothers founded (or refounded) the city Barca (mod. Meri) west of Cyrenaica. After a Libyan revolt against Arcesillaus II it was said that 7000 hoplites were killed. in a battle near Leucon Arcesilaus was killed by Laarchos or Learchos.

His son Battus III followed as king of Cyrene .

Cyrene Vase of Arcesilaus, weighing of Silphium in the presence of King Arcesilaus II of Cyrene 560-c. 550 BC

Herodotus Book 4

This Battus left a son called Arcesilaus, who, when he came to the throne, had dissensions with his brothers, which ended in their quitting him and departing to another region of Libya, where, after consulting among themselves, they founded the city, which is still called by the name then given to it, Barca. At the same time they endeavoured to induce the Libyans to revolt from Cyrene. Not long afterwards Arcesilaus made an expedition against the Libyans who had received his brothers and been prevailed upon to revolt; and they, fearing his power, fled to their countrymen who dwelt towards the east. Arcesilaus pursued, and chased them to a place called Leucon, which is in Libya, where the Libyans resolved to risk a battle. Accordingly they engaged the Cyrenaeans, and defeated them so entirely that as many as seven thousand of their heavy-armed were slain in the fight. Arcesilaus, after this blow, fell sick, and, whilst he was under the influence of a draught which he had taken, was strangled by Learchus, one of his brothers. This Learchus was afterwards entrapped by Eryxo, the widow of Arcesilaus, and put to death.

Plutarch's Virtues of Women

Arcesilaus was the son of Battus who was surnamed Felix, not at all like to his father in his conversation. His father, when he lived, laid a fine of a talent upon him for making fortifications about his house. After his father’s death he being of a rugged disposition (therefore surnamed the Severe), and following the counsels of Laarchus, an ill friend, became a tyrant instead of a king. For Laarchus affecting the government for himself, either banished or slew the noblemen of Cyrene, and charged the fault upon Arcesilaus; and at last casting him into a wasting and grievous disease, by giving him the sea-hare in his drink, he deprived him of his life. So that Laarchus assumed the government, under pretence of being protector to Arcesilaus’s young son Battus; but the youth, by reason either of his lameness or youthful age, was contemned. As for his mother, many made addresses to her, being a modest and courteous woman, and she had many of the commons and nobility at her devotion. Therefore Laarchus, pretending to be her humble servant, would needs marry her, and thereby take Battus to the dignity of being son and then allow him a share in the government. But Eryxo (for that was the woman’s name), taking counsel of her brethren, bade Laarchus treat with them as if she had designed marriage; Laarchus accordingly treating with Eryxo’s brethren, they on purpose delay and prolong the business. Eryxo sends one of her maid-servants acquainting him, that for the present her brethren did oppose the match, but if they could but accomplish it so as to lie together once, her brethren would cease arguing the matter any farther, and would give their consent. He should therefore come to her by night, if he pleased; an entrance being once made in a business, the rest will succeed well enough. These things were mighty pleasing to Laarchus, and he was much inflamed by the woman’s obliging carriage towards him, and declared that he would come to whatever place she should command him. These things Eryxo transacted with the privity of Polyarchus, her eldest brother. A time being now appointed for the congress, Polyarchus placed himself in his sister’s bed-chamber, together with two young men that were sword-men, all out of sight, to revenge the death of his father, whom Laarchus had lately murdered. Eryxo sending at the time to acquaint him, he entered without his guard, and the young men falling upon him, he was wounded with the sword and died; the corpse immediately they threw over the wall. Battus they brought forth and proclaimed king over his father’s dominions, and Polyarchus restored to the Cyrenaeans their ancient constitution of government. There were present at that time many soldiers of Amasis, the Egyptian king; whom Laar chus had employed and found faithful, and by whose means he had been not a little formidable to the citizens. These sent messengers to accuse Polyarchus and Eryxo to Amasis. At this the king was greatly incensed, and determined to make war upon the Cyrenaeans. But it happened that his mother died, and while he was solemnizing her funeral, ambassadors came and brought the news of his intentions to Cyrene. Wherefore it was thought best by Polyarchus to go and apologize for himself. Eryxo would not desert him, but was resolved to accompany him and run the same hazard with him. Nor would his mother Critola leave him, though she was an old woman; for great was her dignity, she being the sister of old Battus, surnamed Felix. As soon as they came into Egypt, as others with admiration approved of the exploit, so even Amasis himself did not a little applaud the chastity and fortitude of Eryxo, honoring her with presents and royal attendance, with which he sent back Polyarchus and the ladies into Cyrene.