The Duel on the Vengeance was a lightsaber duel between Sith Lord Tak Sakaros and his daughter, the fearsome Sith witch Rin Sakaros, which took place in 87 ABY aboard the Devastator-class War Cruiser Vengeance, which was until then Rin's flagship.
The battle on the Vengeance was not the first violent clash between father and daughter. Decades before, Tak's murder of Rin's mother (and his own former lover) Ye'keb Millennium had driven the two to blows. In that first fight, Tak's experience and expertise had trumped his young daughter's superior (but uncontrolled) raw power.
Both due to her disgruntlement at being defeated, and her own inherent thirst for knowledge, Rin set off a few years later on a journey through the galaxy, studying the Dark side of the Force in all incarnations she could find. When she returned to her father, not only had her command of traditional Sith technique swelled enormously, but she also bore a broad and well-developed knowledge of the deep secrets of the Force to boot.
Shortly after Rin's return, she and Tak argued over the direction of the Sith forces, especially in the face of the declining Galactic Alliance and the renewed ascent of the Empire. The argument became hot-tempered, and both cast Force lightning at one another. Eyeing each other testily for a few long seconds, the Sith Lords erupted into battle.
The duel was spectacular, but not long. Much as Count Dooku had, more than a century before, fallen helplessly before the unstoppable fury of Anakin Skywalker, so Tak's lifetime of mastery was insufficient to defeat his impossibly powerful and masterful daughter. Though he employed every trick in the book, utilizing both his extensive skill in combat and much of the environment, Tak was unable to defeat Rin, and she cut off his sword arm above the elbow and destroyed his lightsaber.
Unwilling to yield, Tak attempted to fight Rin off and escape, and in retaliation she cut him off from the Force entirely. Totally defeated, he was left on the Vengeance by Rin, who departed with Tariun Sakaros and his lover, Lorelai, to assume control of the rest of the fleet.
The defeat of Tak Sakaros, his first defeat in a real duel in ages, completely shook up the power structure of the Sith forces. Rin Sakaros assumed the title Dark Lady of the Sith, appointed her brother as the new Steward of Ziost, and received the loyalty of all her father's forces. She began a mission of conquest that was to last for ages and humble much of the galaxy.
Tak Sakaros managed to escape the Vengeance on his personal Z-95, escaping to Borgo Prime. With his extensive wealth, he was able to contact elite Arkanian surgeons, who gave him an exceptional cybernetic arm. At his insistence, they also gave him experimental brain surgery, placing implants in the reflex center of his brain which allowed him to use his lightsaber, though only with a shade of his former skill.