First off, this gives you your exotic sword ON TOP of your legendary. So you have TWO swords. Thank you bungie :)

Anyway, shaxx will send you to the sunless cell strike on the dreadnaught. Clear everything until alakhul. Once in the pit, 3 wardens will spawn. YOU ONLY NEED TO KILL THE ONE WITH YOUR RESPECTIVE ELEMENT TO YOUR SWORD within thirty seconds of killing big boy. So this means if everyone in your team needs the fire sword, go ahead and kill the arc and void warden immediately.

Chip away at big boys and your wardens health until both are nearly dead. Then wipe them with supers, swords, whatever. IT DOES NOT MATTER AS LONG AS YOU KILL YOUR WARDEN AND ALAKHUL WITHIN 30 SECONDS.

Good luck! Thank you bungie.