Cap Increase

Each Lantern Ring has a different cap, It's randomized on world creation and cannot be re-randomized without using commands to do so.

These are all of the tasks you can do:

Kill a Wither - Increases Willpower & Hope
Kill the Ender Dragon - Increases Willpower & Hope
Have Bad Omen - Increases Fear, Decreases Willpower & Hope
Have Hero of the Village - Increases Willpower & Hope, Decreases Fear
Have Darkness/Blindness - Increases Fear, Decreases Willpower & Hope
Be on Low Health - Increases Fear, Decreases Willpower & Hope
Be on Low Health & Swing - Increases Willpower, Decreases Fear