Durga was born in 105 BBY, but suffered the misfortune of having a disfiguring birthmark over his eye. Hutts were notoriously superstitious and his relatives urged Aruk to kill his offspring. Aruk foresaw that Durga would become a great Hutt one day. He then ordered the naysayers to cease their complaints.
Durga reached the Hutt age of responsibility at 100 and learned the business of Besadii at his father's right hand. Durga could see that his cousin Kibbick couldn't run the Ylesian enterprise and asked if he could be sent in his place. Aruk felt that Durga was still too young to go and kept Kibbick on.
After Aruk was murdered, Durga called for help from Prince Xizor to secure the succession and locate Aruk's murderer. Xizor agreed, on the condition that Durga relinquish substantial profits from Ylesia. In desperation, Durga agreed. Xizor had already discovered that Aruk had been poisoned by the Desilijic clan and deliberately thwarted Durga's attempts to uncover the truth. Jiliac Desilijic Tiron, uncle of Jabba Desilijic Tiure and head of the Desilijic clan purchased a rare poison from the Malkite Poisoners and used Teroenza, High Priest of the Ylesian enterprise to deliver the poison to Aruk. Infuriated, Durga squirmed over to the Desilijic palace and challenged Jiliac under the Old Law. Durga and Jiliac fought in mortal combat, and Jiliac was killed. Durga knew that Teroenza was planning independence for Ylesia—he had purchased a turbolaser and hired many more guards. Durga then requested a mercenary force from Xizor to ensure that no trouble would break out and he then hired Boba Fett to assassinate Teroenza and slice off his horn to mount on his wall as a trophy. Unfortunately, the Rebel Alliance had already embarked upon a mission to free the Ylesia slaves and shut down the spice factories. The world was devastated and the enterprise shut down. Durga had to honor his bargain and became one of Xizor's Vigos.
Xizor knew that Durga had enough ambition for ten people and used Guri to keep him in line. Xizor would reflect that greed was good, fear and greed were better. The Hutt became a competitor with Sprax for control over the underworld in the Sisar Run, but some of their conflict was later resolved by the creation of the To-Sharr Uuta Shipworks front as a cooperative venture.
After the near simultaneous deaths of Xizor and Jabba, Durga took over a good portion of Black Sun's assets. With the underworld in chaos following the deaths of the Galaxy's two most powerful kingpins, Durga was able to dislodge Desilijic and make Besadii become the dominant clan on Nal Hutta. He allied himself with the self-proclaimed "General" Sulamar to gain Imperial support on the Darksaber superweapon project. Although Sulamar liked to think of himself as powerful, and also as being in charge of the project, Durga was the mastermind. Also unknown to Durga was the fact that Sulamar was just a lousy Imperial technician. In order to gain information which would be used for his superweapon, Durga ransacked Jabba's Palace on Tatooine for information on how to hack into Imperial databases. He then made official diplomatic overtures to Coruscant asking for peace. As a gesture of good faith, he convinced his fellow Hutts to cancel the bounties on Han Solo and Leia Organa Solo.
During a visit to Coruscant, he brought with him several dozen Taurill. The inquisitive creatures served as a distraction for three of their number to escape and track down and steal the plans for the Death Star. First, Durga offered an alliance and then casually informed the New Republic that the Galactic Empire were up to some very interesting things.
Leia Organa Solo then decided to pay Durga a return visit - it was clear the Hutt was up to something and brought the fleet along for a "training exercise". Durga made his excuses and left for the Darksaber.
The New Republic was fully aware of what Durga was planning and they sent a commando team led by General Crix Madine to sabotage the project using the fleet as back-up. The team failed in their objective and Madine was personally executed by Durga. Before he died, Madine signaled the New Republic Fleet. He also revealed to Durga that Sulamar was just a technician, and a poor one at that. Ultimately, Durga's defeat came about not from the New Republic, but by shoddy construction. The Taurill were used as the builders for the Darksaber but their hive-mind and Durga's cheapness meant that the Darksaber's superlaser wouldn't work. The ship broke up and a hail of asteroids finished off the superweapon, killing the Hutt.
Bevel Lemelisk, the former Imperial engineer whom Durga had hired to design and oversee the construction of the Darksaber, presciently fled the ship before its maiden voyage. As he ran to board his private shuttle, he reflected that, for all the Hutts' vaunted business acumen as crime lords, Durga had committed a grave error by thinking he could build a superweapon at minimal cost.
Indeed, in the aftermath of the Darksaber fiasco, the Besadii clan was severely discredited in the eyes of the other Hutt clans, and the Hutt species as a whole became the butt of jokes around the New Republic for their seeming ineptitude at anything except running criminal organizations.
Two of Durga's three pictures in The Official Star Wars Fact File 124 are actually images of Jabba the Hutt, taken from Star Wars: Republic: Outlander, modified to include Durga's birthmark.