I highly recommend to install the CHAOS;HEAD NOAH Overhaul patch from Committee of Zero (https://sonome.dareno.me/projects/chn-patch.html).
The following walkthrough is based on the translation provided by this patch.

I am grateful to Kiri Kiri Basara and ChrisGLink for their guide which helped me master the game.

Here's my guide to Chaos;Child (the sequel to Chaos;Head):
https://steamhost.cn/steamcommunity_com/sharedfiles/filedetails/?id=3462575790

Unmissable achievements mentioned in the scheme are not listed here.

At 1st playthrough only one route is available.

• Start new game.
  
• When asked questions during the dialogue with Grimm at the beginning of Chapter 1, answer YYY.
  
• Skip all delusions.
  
• In hospital questionnaire (Chapter 2) check all boxes.
  
• In Chapter 6, answer YYY in order to see the bad end. Then load last autosave, give the correct answers (YYNNY), and continue.

After finishing the game you’ll get 10 chapter-related achievements (see scheme), Silent Sky ending, as well as those:


Achievements: 13/34

Now we head on Crying Sky route.

• Start new game. Hint: when skipping, you can Alt+Tab the game, it will not be paused. The default skip settings are pretty good, don’t change them for now.
  
• When asked questions during the dialogue with Grimm at the beginning of Chapter 1, answer NNN.
  
• Select all delusions as negative, except following: ## 2-3, 2-4, 3-3, 5-1 (see scheme). These 4 delusions select as positive.
  
• In hospital questionnaire (Chapter 2) check no boxes.

Make following saves when specified delusion trigger pops up (before you choose the delusion!):

• [Save 1] delusion #1-1
  
• [Save 2] delusion #1-2
  
• [Save 3] delusion #2-3
  
• [Save 4] delusion #3-1
  
• [Save 5] delusion #3-4
  
• [Save 6] delusion #9-1

After finishing the game you’ll get Crying Sky ending and


Load [Save 6]. Read through Chapter 9 and select all delusions as positive.

Achievements: 15/34

Load [Save 1]. Select all delusions as positive except 4 mentioned above: ## 2-3, 2-4, 3-3, 5-1. These 4 delusions select as negative.
Correctly answer questions YNYNY during delusion #1-1.
After finishing the game you’ll get Rimi’s ending and


Achievements: 20/34

From now on you can set the ‘Stop Auto/Skip mode at delusion triggers’ option to ‘Off’. But keep the ‘Skip Mode’ option set to ‘Read-Only.’

Load [Save 1]. Skip delusion #1-1. Correctly answer questions NNYYY. Skip all other delusions (for faster playthrough).
Achievements: 22/34

Load [Save 2]. Select delusion #1-2 as positive. Correctly answer questions NYNYY. Skip all other delusions.
Achievements: 24/34

Load [Save 3]. Select delusion #2-3 as negative. Correctly answer questions YNYYY. Skip all other delusions.
Achievements: 26/34

Load [Save 4]. Skip delusion #3-1. Correctly answer questions YYYYN. Skip all other delusions.
Achievements: 28/34

Load [Save 5]. Select delusion #3-4 as positive. Correctly answer questions YYYYN. Skip all other delusions.
Achievements: 30/34

This variant of Chapter 10 will be accessible from the title menu after finishing all mentioned above. Start it, correctly answer questions YYNNNYYYYYYYYYY when asked.
After finishing the game you’ll get Blue Sky ending and


Achievements: 34/34

It will be accessible from the title menu after finishing Blue Sky.

If you find any issues in this guide, please let me know in the comments.