Undying hate - drop rate and is defeating Vessel of Kulemak at full power required?

Hey,

Dropped my first Kulemak's Invitation in SSF. Main drop I want from the fight is the Undying Hate. So, my questions are:

Do you need to defeat Vessel of Kulemak at full strength for a chance to drop the timeless jewel? If there is a chance to drop it at all difficulties, does the full strength make the drop more likely?

To which existing boss would you compare Vessel of Kulemak or the fight in general in difficulty?