Shortly after I started Act 2, I got a prompt that an Online Vendetta was available. I then looked on the map and found the icon that starts it. It looks like the trophy image. I went to the marker and started the quest.
Your objective is to kill a captain that has killed another player in their game. You don't actually play against another player or see one during the quest, it is purely solo. It is just like taking out any captain in your own game, nothing special needed. Once you defeat the captain, you will unlock this trophy.