To be clear...and avoid any confusion...you only need to keep alive the Hive major with the sword element you need. You can kill the other two and be fine.
I had originally been told to keep all THREE alive AND alak'hul. Doable but such a pain in the ass. I think I may have been trolled come to think of it. BUT, it was for the Raze Lighter so it was worth it :)
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To be more clear: If you are having let's say the solar and void sword quests both on the same character, you can leave both the solar and void knight alive to the end and then slay them and Alak'hul within 30 secs. If you slay one of the knights too early, you will have to repeat the strike for the sword the knight with the corresponding element shield you had killed too soon. ;)