Is "doing a Batman cosplay" idiomatic? Googling it seems to return a few results, but I am not sure if it's idiomatic, because cosplay is a relatively new word and it doesn't really sound natural. Is there a better and more idiomatic way of saying it?
When no other verb seems to fit (or we can't think of the right word) English speakers often fall back on "do".
He does a good impersonation of that famous actor.
They do a nice barbecue at that restaurant.
I heard my favorite singer is going to do a performance at my university.
In that context, it's not wrong to say "do a cosplay":
For ComicCon this year, I'm going to do a Batman cosplay.
However, be aware that "cosplay" is itself a verb:
For ComicCon this year, I'm going to cosplay as Batman.