1. Killer Croc
After defeating Killer Croc, you'll return to the Batcave to reveal Black Mask's goals. Before leaving, talk to Alfred.

2. Sionis and Cobblepot
As I've disabled the second GC radio tower in Bowery before tackling Penguin's men. Fly back to the Batcave and talk to Alfred.

3. Electrocutioner
It happens after you leave the ship. Anarky mission was introduced but I leave it later.

4. Deathstroke
After you've investigated the crime scene in the Lacey Towers, you will be tasked to return to the Batcave to collect a Concussion Detonator. Talk to Alfred before heading back to Gotham.

5. Barbara Gordon
As you will break in and out of the GCPD, and then heading to the Sewers below the GCPD. After revealing the fact that Black Mask was kidnapped by a new criminal, the Joker. Fly back to Batcave and talk to Alfred.
(And Mad Hatter's mission will be introduced as you left the Sewers.)

6. Mad Hatter
After Joker's reveal in Gotham Merchant's Bank.
(This one is a bit unsure. In New Game Plus, Alfred talked about him after I finished a side mission on Mad Hatter WITHOUT finishing the main story first. BUT in my last playthrough, I focus on the main story before doing any side missions.)

7. Large Bat...
Non- story related? Reference of the Man- Bat? In my playthrough, he talked after I've captured Copperhead in the Steel Mill.

8. Bane's tracker
You'll return to the Batcave after arresting the Joker and having some fights with Bane in the Royal Hotel. Take the Glue grenade and talk to Alfred before going back to Gotham.

9. Joker in the jail
After you finished tracking Bane, you'll learn that Bane knew Batman's true identity. And Firefly started his rampage on the bridge.
DO NOT go to the Pioneer Bridge yet. I check back with Alfred before go stopping Firefly.

10. King Bat #1
After finished the main game, talking to Alfred while he's standing on the side next to the training arena. Including this one, I think the conversation about the King Bat has several ones.

<Start doing with the Most wanted mission one by one. (Could be in any order, but here's mine)>

11. Enigma's background
Completed Engima Most Wanted. I return and talk to Alfred, he mentioned about Enigma's background as an employee of GCPD.

12. Tracking Enigma
I complete the Deadshot Most Wanted. I talk to Alfred and this time, he told Batman that it's hard to track down Enigma.

13. Roast Chicken thief
I finish Mad Hatter mission and I talk to Alfred. He said that he prepared a roast chicken but it's stolen by a bat.
(I don't think Alfred's ham one is one of his wisdoms.)

14. Pioneer bridge hostages and Gordon's trust
I finish Shiva mission and then talk to Alfred. He mentioned about hostages, bridge incident and Gordon.

15. Bane's obession
I finish Anarky mission and then Alfred talked about Bane's obsession on Batman.

16. King Bat #2
I finish the Black Mask mission. Alfred talked about the King Bat's outlook, e.g Size. Batman also told him if he should investigate about it.

17. King Bat #3
I finish disabling all of the Penguin's weapon cache. In this conversation, Batman asked if Alfred should continue his study on the King Bat.

<There's One side mission left, it's unlocked by solving all 6 cases>

18. Joker in the jail #2
Solve the first two cases first--- Jezebel Plaza fall and Dixon docks shooting. Then talk to Alfred, he suggested about better security in the prison.

19. Blackgate escapees
Solve the following two cases--- Coventry fire and Burnley hit & run.

20. Introduction of Arkham Asylum
Solve the last two cases--- Amusement mile mauling and Crime alley shootings.
Alfred mentioned about Joker was in jail again and he needed to be watched. And then, he told Batman about Arkham as a safer place.

21. Another thing about bats... dead rats??
I'm quite unsure about this conversation. I quit the game in the middle. As I come back to finish the last mission, I talk to Alfred before going back to Gotham. He gave me this conversation.

22. King Bat #4
I finish Gordon's side mission by capturing all 20 Blackgate escapees. In this conversation, Batman told if Alfred could capture the King Bat.

Well, that's all I've got from Alfred in this playthrough. But I remembered there's also one about Thomas Elliot... the Hush.

It's not a hard achievement, but it's very time consuming as you keep travelling back and forth between the Batcave and Gotham city.