I guess it is the Lucky 13 Cycling badge you are asking about. Did join the challenge and log your rides with a Garmin device November 13-15 and set the activity type to the cycling activity type or any sub type of cycling? Note that manual activities and imported activities doesn't count for challenges. If you post link to your activities and make them public we can check what might be wrong.
Click the open water badge (Just Keep Swimming - Record an open-water swimming activity.) to see which activity awarded you with that badge. It might be caused by using the wrong activity type for an activity. Make sure that that activity got the correct type and the badge should disappear.
I did 13 mile my ride is synced but I did not get the badge.
Was it between 13-14th November, or was it on 15th? If it was done on 15th, edit it and change the date to 14th. If it does not help, post the link to that activity here. Also - did you previosuly explicitly join the Lucky 13 Cycling Challenge?
I also have an open water badge and I have never swam open water
Which badge exactly? What is its name - Just Keep Swimming, or something else? And what activity exactly does it tell the badge was awarded for? Open the badge in Garmin Connect Web - the details always show a link to the concerned activity, so make it public and post it here.
