In the video below, Esoterickk performs the first solo kill of Oryx in Hard Mode.
Now, a 335 Sleeper can stagger Oryx in Hard Mode which makes a solo kill possible.
If you’ve wanted to tray and kill Oryx in Hard Mode all by your lonesome, this Destiny player has accomplished the task and recorded it for posterity.
Esoterickk goes into more detail on his strategy in a reddit post, and lists the following requirements which need to be met in order to best Oryx solo.