Setting up badges can be complicated. WOS allows badges to be set up when players complete a difficulty, join the game, make it halfway, or beat it completely.

You Played, Halfway, & Winner

Go to the Configurations module. If you've already set up WOS, it should be in game.ReplicatedStorage.WOS. Open the script and scroll down to the 'Badges' table. Under the table, you will find the keys Joining, Halfway, & Winner. You can replace the '0' with your respective badgeIDs.

Difficulty

This is a little more complicated. While in the Configurations module, under 'Badges,' find the key 'AwardPerStage'. If you haven't made any changes, you should see the default values. If not, use this:

Effortless = {AwardedStage = 20; ID = 0;};

You can set "Effortless" to anything, as long as it's not the same as another key in that table.
Replace 20 with the number you want the badge to be awarded at.
Replace 0 with the badgeID.