Unable to start second part of quest.

[Leania]

I've tried looking up some information on Blood's Honor quest, was able to complete the first part, however after returning and speaking with Vilkas, Purity of Revenge does not start. I have Retrieve the Helm of Winterhold, and I read that you have to complete this quest before initiating Blood's Honor. Is there a way to initiate Purity of Revenge if one has already started Blood's Honor while having Retrieve the Helm of Winterhold?

 

If not, is there much loss from not completing the set of Companion quests?

 

Thanks