In order to win this battle you only need to bring her down to half health, so use lightning attacks to finish the fight quickly. Switch to the Contention battle stance which works well against Jedi. After dealing with the Red Eclipse you will be approached by a woman member of the Sith who will attack you.
You can control the slave trade from the cantina on Nar Shaddaa in the future. This is not only a choice dark side move, but it will net you profits in the future. Tell him that you could kill the Red Eclipse easily and then take control of their slave trade. Slash through the ranks until you encounter the leader of the group who will speak to you. Many more members of the Red Eclipse are on the ship waiting to do battle.
Boarding the Ebon Hawk is the only way to advance the story line. The entire walkway to your craft is lined with these enemies so prepare yourself for a long battle. When you return to the ship there will be a group of thugs waiting for you known as the Red Eclipse.