The last two planet that I have invaded I have not received green badges for... I have been stuck at 13 and I am trying to get my second Atmospheric Decimator. This is not the first time I attempted to invade either planet but it was the first time I was successful, so I know it was not because of the rule that you can only get a badge for taking a planet once every week. Can you tell me if there is a known bug or if I can get these badges somehow?

Thanks!

Failing an invasions counts toward the once a week thing. Also if you invade a planet of the same owner.

Yep, if you invade a planet but fail and then try again tomorrow, you won't get a badge because it's an invasion attempt on the same owner within a week.

You don't get a badge from taking any planet from a player you have attempted an invasion from in the past week.
So in addition to failing an invade and successfully invading the next day not yielding a badge, you will also not get one if you invade an entirely different planet from the same player.