Try some of the suggestions from the wiki
elderscrolls.wikia.com/.../Boethiah%27s_Calling
Sometimes after killing the follower on the pillar, Boethiah's conduit will not start the dialogue with the player, making the quest impossible to continue. To fix this, just kill all of her worshippers. Then she will leave your companions body and go
to the last worshipper you killed. Then you can actually talk to Boethiah's reincarnation and continue the quest as usual.(Xbox360/PC/PS3 confirmed)
If you cleared out Knifepoint before you get this quest, it is possible to have the quest not move past the stage where it is telling you to kill everyone. If this happens, you may be able to move the quest along by putting on the Ebony Mail you get from
killing the leader, but this does not always work.
If you open your journal while Boethiah is in possession of one of your companions, or one of her followers, it is possible for the visual effect to never end. Reloading an earlier saved game will fix this.