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That's your "perfect month" award. You will achieve it by filling the activity (red) ring every day of the month and then the badge will turn gold. It's under the "complete your rings" section.

The monthly challenge badge looks exactly the same when not completed but will turn silver upon completion. It is also a more specific challenge, like walking/running a distance, completing a number of workouts, getting 200% move goal for a number of days etc. This one is under the "Monthly challenge" section, above the "complete your rings" but below the "special challenges" section.

Thanks for explaining it :)

I don’t have a monthly Challenge section in the activity app. :(

I was thinking of downgrading my phone iOS 12. Then restoring my backup I saved on my computer from itunes instead of iCloud and see if that helps my issue.
 
All of my missing Monthly Challenges magically reappeared just after midnight tonight. I guess the generation of the new month's challenge somehow triggered a refresh of the list.

My friend, who had the same problem, also got his back. How about you guys?

Same, all of mine came back today!!
 
Something interesting here with two new iPhone Pro 11's and AW S4. Yesterday I activated my partner's new iPhone 11 Pro and re-paired here AW S4. The last day (Sept 30) of her monthly challenge disappeared and she was concerned she wouldn't get it. Today it popped back up and said she completed it. Now I have the opposite of stories...

I set up my new phone today and repaired my watch. Now this morning on my watch with OS5 and my old iPhone 8 Plus, my original monthly challenge (Oct 1) was to close all three rings 25 times in October. After activating my new phone and syncing the watch, my challenge CHANGED to burn 30,800 calories during October.
 
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