Didn't get the achievement like that, so i started another attempt and that ultimately made me succed in ending the game.
Start the game offline and talk first to Frank, who asks you to look for your horse, you do so immediately, as soon as you find your horse, come a short dialogue and end the conversation.
With the Y Button you sit on your horse and that's the said place where you take a rubber to hand.
And so that you run in a circle. From here the Days does not end and so no savepoint is created.
Plug the Controller into the console and let it run for 24 hours without you having to do anything.
And you can do what ever you like;)
**Importantly, the console must not be turned off in any case, otherwise the progress does not count.**
After you have run the game 24hrs, the icon is still not shown in the Journal, this only happens when you have spoken to Frank again afterwards.
Edit: Wait after the Cleaning Minigame then the Icon shows up in your Journal.
Thanks goes to A 0 E Monkey for the Tipp.
Then goes back online and the achievement is yours.