She was the daughter of and the elder of Cleopatra III’s sons Ptolemy IX Soter and probably Cleopatra Selene I.* She married her uncle Ptolemy X Alexander in 101 BCE, when she was somewhere between the ages of 15 and 20. This was only a few years after he took the throne from her father (his elder brother), at the behest of his mother Cleopatra III. Shortly after the marriage, he had his mother murdered.
Berenike had one child, possibly Cleopatra V, with Ptolemy X, but she also became stepmother to his son Ptolemy XI Alexander. Their reign lasted until 88 BCE when Ptolemy X returned, took back his throne, and expelled them from Alexandria. Berenike didn’t stay away long though and was able to return sometime before 81 BCE. It’s possible, though not certain, that she may have co-ruled with her father during the last few years. Some scholars even claim that he married her, but this seems less likely.
On her father’s death, Berenike briefly became sole ruler of Egypt. Her reign lasted only six months before her stepson Ptolemy XI returned from Rome to take the throne and marry her. Berenike’s status as both daughter of one previous king and wife of another granted legitimacy to bother her own rule and Ptolemy XI’s and it didn’t help that she was extremely popular with the people of Alexandria. But her marriage and co-rule with Ptolemy XI didn’t last long. Only 19 days after they married, Ptolemy had her murdered, only to die himself at the hands of a mob of angry Alexandrians, who had loved their queen. The throne passed to Berenike’s half-brother Ptolemy XII.**
*It’s also possible that Cleopatra IV, not her sister Cleopatra Selene I, was Berenike’s mother.
**Who might have been illegitimate.
Pausanias, Description of Greece 1.9.3 - Perseus
Eusebius, Chronicle 1.165 - Attalus.org
Berenice III - Egyptian Royal Genealogy
Cleopatra Berenice III - Livius.org