Courtesy of @Boubou:
Ever since Visions were introduced, I get my Avarice Conquest without even trying. Especially on T16. I’ll clear Visions while running Bounties. When you hit a map with Goblin Packs, kill them as quick as you can. Your Pet will pick up most of the Gold. The rest you can pick up while chasing down the Goblins. Don’t pick up any loot until all the Gold has been picked up or you see the Avarice Conquest Complete popup window.
I do this with my Unhallowed Multishot Demon Hunter and no special “Gold gear”.