And so, after 10 minutes of climbing through the discussions on English-language and Korean forums, I found a solution to the problem that there are no achievements in the current version. It turned out to be very simple.

In the folder with the game, we throw the old version of the game in 2017 (Everything works fine, immediately received an achievement for the first entry into the game)
BE SURE BEFORE INSTALLING THE PATCH > Turn off Steam cloud for this game.
This is done in the following way Library>Dragonia>Properties>General>Uncheck steam cloud
The path to the game is Steam\steamapps\common\Dragonia\game_Data it is in the game_Data folder that you copy all the files with the replacement.
I do not recommend deleting the folder and replacing it completely.
Actually here is the link to the old patch of the game:
https://disk.yandex.ru/d/pmjm81of-PbLGw

IN CASE YOU STILL HAVE A BUG IN THE SECOND CHAPTER OF THE GAME.
There is a bug when switching between illustrations, or rather at the end after our heroine receives another portion of white matter.
Decision.
1) alt+f4 or via the task manager.
2)To get this achievement, download steamachivementmanager
But use it at your own risk. I do not advise you to abuse this program. I only advise you to use it in order to get this achievement.
Game ID for steamachivementmanager [635730] without quotes.
If you just want to go to the second stage, repeat step 1. And through the selection of levels, go to the second chapter of the game.

I share that I really managed to do everything.
Promote this guide to the maximum, share it with your friends, suddenly they are also hunting for these achievements for a very long time :)
Have a good day :)