You can get this amulet after completing the main quest line and then returning to
The Lair of Infinite Agony. There will be a yellow exclamation point on the map, go to it.
You will see an NPC named
Mr. Miz, accept the quest
The Amulet from him.
He will give you the options to either purchase from his shop or you can choose to hit him. Choose to shop from him and you can purchase the Mysterious Amulet. Once purchased, equip it and you will receive your trophy.
The cost of the amulet scales with your level, just like all other items in the game. I was level 51 on TVHM and it cost me $840,000. The video I included below has the guy at level 61 in UVHM and it cost him in the $3,300,000 range. So make sure you have plenty of money.
If you're curious about this amulet and its effects, check out the wikia page regarding it. Its effects are currently unknown and its usage in game is widely speculated.http://borderlands.wikia.com/wiki/Mysterious_Amulet