Shade of Akama is the second boss in The Black Temple, and some players have reported problems with finding out how to begin the encounter. When you enter the room where Shade of Akama is located, begin it by quickly clearing out all the enemies in the room. Once this is done, Akama (the real one, not the shade) will spawn close to the entrance to the room. Speak with him to begin the encounter.
And that's how you begin the Shade of Akama encounter in The Black Temple. It's very easy once you know how.