TLDR; The Handsome Jack AI is the main antagonist of the video game Tales From The Borderlands. He is exactly like the original Handsome Jack but he can only be seen by Rhys (the player character) as a ghost-like blue hologram. He was voiced by Dameon Clarke, who also voiced the original Handsome Jack.
The best place to learn all about Jack before he became AI is through the Borderlands Wiki.
Scenes from the game: Skin Pizza Party, Jack and Rhys are BFFs, Even more scenes
When Rhys attempted to use Professor Nakayama's ID drive to track the money he lost, Rhys accidentally downloaded the Handsome Jack AI into his own brain. This gave life to the new Handsome Jack as he awoke inside the mind of Rhys, Rhys is the only person that is aware of the new Handsome Jack.
The hologram clone was created by Professor Nakayama to continue the legacy of Handsome Jack and his plans to create a better world for Pandora. Initially, the Jack AI does not realize nor believe that he is dead and even attempts to strangle Rhys but that proves ineffective as he phases right through him. He tells Rhys to bring him back to Helios so he can be transferred into a new body, lying to him and saying they can both run Hyperion "together".
Jack later upgrades Rhys' Echo-Eye implant to give him the ability to hack into machinery and control it at his will. When Rhys and Fiona finally discover the Gortys Project's location, they are attacked by numerous sentry drones, which Rhys has a choice use for his assistance against Vasquez and August. If he chooses to do so, Jack will take control of them by merging his consciousness into Rhys'.
In the final episode, the Jack AI forces Rhys to assume position as Hyperion's CEO and reveals that it intends to create a fleshbot army out of him and many others by downloading himself into all of them. The plan fails and Helios crashes into Pandora, destroying everything the original alive Jack had built. Jack has one final confrontation with Rhys after a talk about his dead daughter and he eventually downloads himself into Rhys' cybernetics again. Jack starts to strangle him with his own robotic arm, but Rhys manages to rip off his arm.
While Jack threatens to eventually kill him, Rhys rips out all his cybernetics with a shard of glass. Jack then begins to beg on his knees for his former fan to spare him, but Rhys pulls out the echo eye. In one last, desperate attempt to kill Rhys, Jack tries to stop him only for Rhys to rip it out the last of his echo eye, severing Rhys' connection with Jack. Jack disappears and is trapped inside the echo eye, leaving Rhys to decided his fate.
If Rhys decides to kill him, he crushes the eye with the palm of his hand, destroying it along with the AI of Handsome Jack which finally kills him once and for all. If Rhys decides to keep him, he puts the eye in his pocket, leaving the A.I. of Handsome Jack trapped inside it forever.