You have to complete the Taken King Story DLC and you need Rank 3 in crucible to obtain the Quest from Amanda Holliday. Here are the Steps to obtain this exotic weapon:
00:06 – Step 1: Equip the Last Word and your favorite class super, special and heavy weapon. With the Last Word equipped, killstreaks
achieved with your special weapon or heavy weapon or class super also count towards the quest progress. Single class super, special
or heavy weapon Kills do not count but the killstreals or double downs (as example) also count towards the quest progress.
The higher your killstreak, the more you get % for the first step.
02:40 – Step 2: Speak to Amanda Holliday in the Tower Hangar
03:19 – Step 3: Purchase a generous Donation (cost 15000 Glimmer)
04:03 – Step 4: Bring the donation to Amanda Holliday
04:34 – Step 5: Use Shotgun to defeat Guardians in Crucible or against yellow high enemies in PvE. Play PvP because you receive 3% for each kill and
there is no punishment if you die. In PvE you receive only 0.25-0.5% for each yellow enemy (except Bosses – 6%)
05:21 – Step 6: Speak to Amanda Holliday in the Tower Hangar
05:52 – Step 7: Use a Shotgun to defeat the Shield Brothers on the Dreadnaught. It is a separate 290 strike with matchmaking. You really need a good fireteam!
It is enough if you use the shotgun on the last life of the brothers
06:42 – Step 8: Speak to Amanda Holliday in the Tower Hangar
07:19 – Step 9: Wait for the next weekly reset
07:35 – Step 10: Speak to Amanda Holliday in the Tower Hangar
08:20 – Stats and Gameplay