Depends where you are and the swim programme they follow. Some offer badges at different points to others. Ours didn't offer distance badges, but you could purchase badge and certificate for each level when they passed.
Dd started swimming shortly after her 4th birthday. The first sessions were called ducklings and there were 3 levels. They covered lots of things around just being in the water, putting your face in, being safe etc, as well as the start of strokes etc. Badges for those were gained much quicker.
The other levels dd took much longer to progress through. Took ages to pass level 1. Not anything being done wrongly, but was stuck on one specific skill for a long time. However she carried on and worked her way up.
Whilst thrh only had badges when thry passed a level, we could see on the app each time she progressed in or passed a new skill, so that was motivating to her. She could see she was getting closer to passing the level.
Others progressed through levels (especially lower ones) much quicker, but dropped out before completing all the levels. Her progress was slower, but she kept at it, and ended up in a swim club doing competitions.
Is there an spp or anything you can check her progress on, so she can see if she is getting closer to a badge.
Do they offer lessons in the school holidays. We paid gor 30 minute sessions each day for a week in the school holidays. They were great for progress because there often ended up being a few less children than a normal lesson. She had some weeks where there were only 2 or 3 in the session, and at least 2 weeks where she had one to one (those weeks she passed levels because the instructor could focus on only the skills she needed to pass).
I would talk to the instructor and see what they say.