If you want a cool sword in Destiny: The Taken King and a legendary one at that you need to complete certain quests. The sword is an elemental one and you get to choose between void, arc and solar.
First of all, you need to complete the main story missions of The Taken King. Once you do that, you can go to Eris Morn in the tower and get a quest that requires you to go to Lord Shaxx. He will give you a quest that requires you to go to The Dreadnaught patrol and obtain 25 Hadium Flakes from chests.
It’s a bit difficult because the area is huge but we have a good farming method for it which you can check out below.