Need help finding this outfit

MuzMel

The main piece she wears under the jacket. I don't know what it's called in English and I can't find it!

 

The Blurst of Times

I'd call it a "leotard", with fishnet stockings.

It's not quite a catsuit or unitard, but searching on those might bring acceptable results.

Here's one in this store.
https://www.daz3d.com/dforce-ballet-practice-outfit-for-genesis-8-females

In this store...vyktohria has a geo shell that would work.
https://www.daz3d.com/sexy-skinz--bodysuits-collection-for-genesis-81-females

Hardly an exhaustive list.

If I had to choose one, I'd look at OneSix's store at Renderosity.

FSMCDesigns

There quite a few both here and at rendo. here are some that might work for you. Stay away from sites that sell copyrighted versions of the actual black canary outfits (ripped from games)

https://www.daz3d.com/pretty-bunny-outfit-for-genesis-8-and-81-females

https://www.daz3d.com/bunnys-nightmare-outfit-and-poses-for-genesis-8-females

https://www.daz3d.com/bunny-girl-costume-for-genesis-3-female-s

 

pwiecek

Bodysuit 

solisphotography

You could use the bodysuit from this:

https://www.daz3d.com/charlene-character-hair--clothing-bundle

You would need to delete the "Trim" surface as well as "Cloth3" and the best news, it just went on sale

Fauvist

I'd call it a corset.  And from your first example image, it looks like the corset operates like a "push up" bra.  Take a look at this https://www.daz3d.com/seductive-girl-for-genesis-8-and-genesis-81-female

There's also a lot of similar and or useful clothing by the artist who made this https://www.daz3d.com/seductive-girl-for-genesis-8-and-genesis-81-female

The name of the garment is cultural - depending on which country you are in, and also what time period you are talking about.  In Canada a sweater is called a jumper in England.

When you do a Google Image Search for "Black Canary" and leotard - a lot of pictures show up, the same when you type "Black Canary" and corset.

For the "push up" feature, check this out https://www.daz3d.com/i13-swim-duo-bikini-and-one-piece-for-the-genesis-3-female-s