What is the fastest way to complete "The Art of Conversation" achievement?

I know from reading this question how to finish up the follower conversations, however to get "The Art of Conversation" I need to complete almost all conversations in the game (I believe there are a handful that don't count). I've beat the game at this point, so I believe all conversations should be unlocked, but I see that I can't simply proceed to the last mission in each Act to get all conversations from the other NPCs. I am genuinely interested in hearing all of the conversation, but I'd like to perform a "speed run" in which I make the minimum number of stops to get them all. Actual speed is not an issue, I just want to maximize efficiency.

The ideal answer will specify the minimum stops in terms of events/quests/acts to gather all conversations.

Solution 1:

Based on a rough timeline of the data I collected, there are 23 points during the game that have to be hit to complete all the conversation achievements and, because of dependencies, they need to be hit in order. When talking to someone, you are expected to complete all their available conversations before moving on to talk to someone else, but I only count the conversations that count towards achievements despite there being additional extra conversations available. I will try to group conversations to cut down travel time, making this pretty close to the fewest stops with the least travel, but there is probably some room for optimization once all dependencies are mapped out. Don't worry about avoiding people with asterisks because you will get those conversations later and this way involves less running around. I'll go through and confirm specifics and nuances later to determine if there are inconsistencies to timing and number of conversations based on current objective and dependencies.

Act I

The Fallen Star - Rumford at the Gates: Takes you right to town. Talk to Haedrig and then Leah for 1 conversation each.
The Legacy of Cain - Begin Quest: Talk to Leah to begin the quest. Talk to Haedrig and then Leah for 1 conversation each.
A Shattered Crown - Begin Quest: Talk to Haedrig for 1 conversation. Talk to Deckard Cain to begin the quest and then talk to Leah for 2 conversations, Deckard Cain for 4 conversations and then Covetous Shen for 4 conversations.
Reign of the Black King - The Royal Crypts: Talk to Haedrig for 2 conversations and then Covetous Shen for 1 conversation. Deckard Cain has a conversation that you get by completing the quest, but you should have this one already since you beat the game - if you want to re-listen to it, you can get it at the next point.
Sword of the Stranger - Khazra Den: Talk to The Stranger for 1 conversation, then Deckard Cain for 2 conversations, and then Covetous Shen for 1 conversation.
The Broken Blade - Talk to Alaric: Talk to The Stranger for 1 conversation. You will need to run through the act a bit to get Leah's 2 conversations as she follows you, 1 while collecting beacons and 1 at the drowned temple.
The Doom in Wortham - Begin Quest: Talk to Deckard Cain for his last 4 conversations, and Haedrig and Covetous Shen for 1 conversation each. Talk to The Stranger to begin the quest. Talk to The Stranger again and then Covetous Shen for 1 conversation each.
Trailing the Coven - Khazra Barricade: Talk to Leah and then Covetous Shen for 1 conversation each.
The Imprisoned Angel - The Cursed Hold: Talk to Covetous Shen for 1 conversation.
Return to New Tristram - Begin Quest: Talk to Tyrael twice, Haedrig, and then Covetous Shen for 1 conversation each.

Act II

A Royal Audience - Begin Quest: Talk to Eirena for 3 conversations, Haedrig for 3 conversations and then Covetous Shen for 6 conversations.
Blood and Sand - Begin Quest: Talk to Leah for 3 conversations, Adria for 9 conversations, Tyrael for 8 conversations, and Covetous Shen for 1 conversation.
The Black Soulstone - Realm of Shadow: Waypoint to The Archives of Zoltun Kulle and talk to Leah for 1 conversation.
The Scouring of Caldeum - Begin Quest: Talk to Adria, Haedrig and Covetous Shen for 3 conversations each.

Act III

The Siege of Bastion's Keep - Light the Beacons: Talk to Tyrael for 2 conversations. Town Portal. Talk to Haedrig for 3 conversations.
Turning the Tide - Begin Quest: Talk to Tyrael to begin the quest. Talk to Tyrael for 4 conversations and Haedrig for 1 conversation. Enter the Armory and talk to Adria for 2 conversations and Leah for 3 conversations.
The Breached Keep - Find the Breach: Talk to Tyrael for 3 conversations and Kormac for 11 conversations.
Tremors in the Stone - Begin Quest: Talk to Lieutenant Lavail to begin the quest. Talk to Haedrig for 1 conversation and Covetous Shen for 7 conversations.
Machines of War - Destroy Ballistae: Talk to Haedrig and Covetous Shen for 1 conversation each. Enter the Armory and talk to Adria for 1 conversation.
Heart of Sin - The Second Heart: Talk to Haedrig for 1 conversation and Covetous Shen for 2 conversations.

Act IV

Fall of the High Heavens - Begin Quest: Talk to Tyrael several times for 3 conversations. Use the nearby waypoint to Bastion's Keep Stronghold. Talk to Kormac for 4 conversations, Lyndon for 14 conversations, Eirena for 8 conversations, and Covetous Shen for 3 conversations.
Beneath the Spire - Begin Quest: Talk to Haedrig for 2 conversations and Covetous Shen for 3 conversations.
Prime Evil - Enter the Crystal Arch: Talk to Lyndon for 1 conversation, Eirena for 2 conversations and Covetous Shen for 1 conversation. Use the Waypoint to go to The Pinnacle of Heaven and talk to Tyrael for 5 conversations.

Solution 2:

Followers
Templar "For the order"
Scoundrel "To catch a thief"
Enchantress "Secret of ages"

Blacksmith "Hassling Haedring"
Jeweler "Everybody loves Shen"
Merchants "Sales and tales"

Main characters
Deckard Cain "Stay a while and listen"
Leah "More than stories"
Tyrael "It's just us"
Adria "Bewitched"

Solution 3:

The comments on each of the achievements at d3db.com has an extensive list of all the points where you can get each conversation. It took me an hour or so to work through them all.