The polystyrene figure had a hole in its back from the casting process. I closed it with a small piece of polystyrene. Here the hole is nicely covered with sequins and there's no more trace of it.

One thing I hadn't thought of is how thin the fins are. I couldn't simply push a needle in - it came out at the back (and several did before I noticed). So I had to insert them in weird angles and it required a lot of care.