Humanity

The Yellow Core is unlocked after completing Sequence 6. It consists of 5 levels, the first 4 being puzzles, and the final being a boss fight. As you fight this boss, you will do damage to them and gain more followers in return. When you take damage, you'll lose followers. You need to defeat the boss by doing enough damage without losing all your followers.

Here is a full video walkthrough with all solutions, all Goldys, and achievements! (Timestamps in YouTube Description)

Story related Boss Battle
Work your way in close to the Yellow Core, it is being held up by like a cone shape of "Others", if you get in close enough you can kill enough "Others" to make the Core collapse, there are a few waves of doing this until you finally destroy it. Be careful not to lose all your humans or you need to restart the battle. Here's how I did it and I picked up the Follow the Leader achievement too:

3:28:52 – FOLLOW THE LEADER ACHIEVEMENT & YELLOW MELLOWED ACHIEVEMENT

Full Walkthrough for all achievements, timestamps for all achievements are on the video chapters

Story related Boss Battle
Work your way in close to the Yellow Core, it is being held up by like a cone shape of "Others", if you get in close enough you can kill enough "Others" to make the Core collapse, there are a few waves of doing this until you finally destroy it. Be careful not to lose all your humans or you need to restart the battle. Here's how I did it and I picked up the Follow the Leader achievement too:

3:28:52 – FOLLOW THE LEADER ACHIEVEMENT & YELLOW MELLOWED ACHIEVEMENT

Full Walkthrough for all achievements, timestamps for all achievements are on the video chapters