Quite well done for an Idle game, and using the setting, monsters, everything of Cloudstone gives a feel of playing Cloudstone along the way, which is nice.
You can't get the Fresh Fish for Feisty Felines Badge that's been input if you were already past there. For example, I'm level 36 (I was 35 when the badges were added), but I can't get the level 5 badge.
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You got the badge. The game submits your level as soon as you start a run.