In the spirit of discovery, these steps are made as vague as can be.
Enjoy them at your own pace, stay off social media, and have fun with Chapter 3.

1. From the chapter start, progress the story until you see a score counter. You'll know when.
   
2. Get S-rank first-try or buy it afterward from an NPC south of the green room.
   This NPC can only be used once!
   
3. In the green room, there are two doors up north. Enter the obvious one. The left one.
   
4. Talk to the NPC in front of the big door and enter THE ROOM. This is what we will be calling this place, so keep that in mind.
   
5. Once inside THE ROOM, move left and you'll know what to do from here.
   
6. Find an item and use it (on stuff) until your meter says "MAXED".
   
7. Do not go back to where you began. Go back to where you changed areas, with a forest up north, and use your item to go up into it. Eventually, you'll find something. Interact with it.
   
8. Continue the story. Get S-Rank first-try yet again.
   If you didn't buy a rank from the NPC before, you can do it now if you need it.
   
9. Go back to THE ROOM and head inside again. Continue until you can't.
   
10. Continue the story until you get back to the green room.
    This is your last opportunity to get Chapter 3's egg! After Step 11, it's softlocked!
    
11. Go back to THE ROOM one last time. Continue until you can't.
    
12. You may now continue the story freely. To get the shadow crystal, win a seemingly unwinnable fight. You will know it when you see it.

tl;dr, get two S-ranks and inbetween story bits, whenever you find yourself in the green room, visit THE ROOM and continue until you can't. Visit 3 times in total. Visit #1 is after the first S-rank. Visit #2 is after the second S-rank. Visit #3 is later.

Alternatively, you can get the lowest score to get Z-ranks. Talk to the Zapper in the ABC room to unlock a room that you can access a manhole cover from. This takes you to THE ROOM!
Either approach works just fine, getting access to THE ROOM is all that is needed.

tl;dr of the tl;dr, consult... THE GRAPH.

• The win condition is a damage threshhold, not "last X number of turns".
  
• You can't pacify, only fight. This fight does not affect pacifist runs.
  
• Have Kris and Ralsei Defend every turn they can to build up TP.
  
• Then, spend that TP on Susie's Rude Buster every single turn!
  
• Stock up on the best food and in particular bring revive mints due to something quirky.
  
• You may notice that Kris is not as affected by the "quirky" part of this fight, so Susie makes best use of what you obtained in the steps above.
  
  If you have any questions at all, feel free to post them below and I'd be happy to clarify!