Worst Moon is one of the 4 modes in Battle Arena. It gives you a bigger reward, but decreases your stats. It's also required for secret things.
How to enter
There are 2 ways to enter Worst Moon mode.
Worst Moon Gem
Combining the 2 ways (Apocalypse Mode)
Combining the Invisible X ally with the Worst Moon Gem results in entering a new mode: Apocalypse Mode.
Information about this mode can be found here.
Rewards & Negative Effects
A full list about the down- and upsides of Worst Moon can be found here.