"Storyteller" requires you to talk with Calendar Man on 12 specific days of the year. He is located in the basement of the Solomon Wayne Courthouse which is where you save Catwoman at the beginning of the game. The Calendar on the wall outside of his cell has each date that you need to visit him circled.
Since this game came out in October 2016 thats where I'll start. Not that anyone reading this is going to wait to get this legit lol.
Edit: I've updated the dates for 2021 and only listed the dates that change for 2022.
2021
-January 1st, New Years Day
-February 14th, Valentines Day
-March 17th, St. Patricks Day
-April 1st, April Fools Day
-May 9th, Mother's Day*
-June 20th, Father's Day*
-July 4th, Independence Day
-August 16th, St. Roch's Day
-September 6th, Labor Day*
-October 31st, Halloween
-November 25th, Thanksgiving*
-December 25th, Christmas
2022
-May 8th, Mothers Day*
-June 19th, Fathers Day*
-September 5th, Labor Day*
-November 24th, Thanksgiving*
*Every Year these dates will change so verify with the calendar next to his cell for dates beyond whats listed.
Now onto how to get this Achievement in about 30-45 minutes by changing the date manually, instead of waiting a year like intended.
- First go into your
Settings ,
Network Settings and click
"Go Offline"- Afterwards power your console down (mine isn't set to instant on) otherwise the console won't let you change the date.
-When your Xbone is back on go into
Settings,
System,
Time -
You can now change the date to one of the days listed above and your ready to go.
Once in game enter through the back of the courthouse. This will be the load zone that we will use to save our progress each time we talk to Calendar Man. Go down, listen to what he has to say (some of its pretty messed up lol) then exit the building out of the same door we came in through. Once it saves hit the dashboard button

, then

, click
All Settings and change the date to another one of the specific days. Once done hit

and you can go back to Batman who will just be chilling outside the door to the courthouse. Never even needing to save/exit your game to change the date. Rinse and repeat. The game will track your progress by crossing out the months on the Calendar next to his cell.
Final note, I did this on Halloween, so I left that date for last and connected back to Xbox Live to automatically change the date before popping my Achievement. If your trying to do this on a day not listed then connect back to Live after hitting

to talk with him one last time. The Chievo should pop before he's done talking.
Good luck and Happy Hunting!
EDIT: Credit goes to
NapoEarth for pointing this out as a solution to some issues people are having while visiting Calendar Man on the correct dates but being told to come back another day.
It appears, after looking at the comments, that the date goes by GMT and your local time zone means nothing. This means that, depending on the time of the day, it will either work or you will be one day ahead or one day behind depending on where you live in relation to GMT.So essentially it seems that the game doesn't go by the players time zone and instead sticks to a standard time no matter where you live. Which is causing issues with Holidays not falling on correct days for some.
I don't know why I didn't think of it earlier but thanks to
The Dawn of Don heres a link to a website that will give you the current time for the GMT Timezone. You can also look up Holidays on this website.
https://www.timeanddate.com/time/zones/gmt