Don't you need to find the resources first and then kill Alak'hul and those guardian knights? I don't quite remember. There is however one step that just requires you to kill three hive majors on the Dreadnaught to open a door to an area where you will find another major you need to kill with a sword (legendary will do). The Alak'hul strike works differently. Three hive majors, each with a different shield (void, solar, arc) will spawn there. You need to keep all alive whos shield corresponds to the element of one of the swords you are having a quest for on the character doing the strike with until you can kill them and Alak'hul within 30 secs (majors first, then Alak'hul).