If I have some time after work I might dig around more and try to identify something similar for you, but here's what I've gathered from that photo:
- it appears to be a stretch fabric
- there is some heavier structure underneath (boobs don't do that in stretch fabric, and you can see the area under the belt where the front of the bustier attaches and that's clearly a stretch with no support)
- it has some kind of pearlized finish
The pearlized finish is the sticking point here -- I can find plenty of metallic purple, and mystique dot purple, and some wet-look purple, but I can't find anything that isn't SHINY or super shimmery that has that pearlized effect. It could be a vinyl, and that's something I haven't had time to search for yet (but now that I'm telling you, you can do that yourself I guess). It could also be latex, but from my cursory look before getting to work, it seems to have too many actual seams for that.
Regardless, if you want the shaping that the original reference has and that the cosplayer you posted has, you'll have to create a more structured garment and then use your decorative fabric on top, just as a finish. A leotard isn't going to do it for you here.
Have you tried asking the cosplayer what the fabric is? A lot of cosplayers are happy to help, so it's worth a shot at least. Or you can dig through their social media and see if there's any WIP posts that might help.