Complete LionFang's 13LoC chapter (Map > Story). This includes /blackhorn > /onslaughttower > /falguard > /deathpits > /venomvaults > /stormtemple.
Accept Logash's "Rotstone Daggers", "Logash's Line", and "The Drums Of The Dead" quests from /deathpits. Then go down the ladder to the left and farm the 3 Rotting Darkbloods. Turn the quests in as you get each drop.
Complete Sir Valence's "You've Been Noticed" quest at /venomvaults. For it, just keep walking left until you find 2 Chaonslaught Casters and farm them. If you're an advanced player, consider the below method. Also make sure to enable Quest Log Turn-Ins and Reaccept Quest After Turn-In from Advanced Options. This way you can keep your Quest Log open and turn in quests from there. You can access your Quest Log by pressing L.
If you're high level and have a strong soloing class (or you're in a group), accept Logash's "The Chaos Eye of Vestis" and "Bone Ladders" quests at /deathpits. Then just farm Wrathful Vestis (you can get to them quickly by pressing the arrow pointing downwards at the top-right). Because the Chaos Eye isn't a guaranteed drop, if RNG isn't on your side, the method at /venomvaults will be faster.