Hi,
I'm assuming these are two different garments.
corpetto a manica corta:
bodice with short sleeves or short-sleeved bodice, as you prefer (odd description, but there you go).
top con balconcino: strapless top. I've also seen this called a "bustier" in English. It basically looks like a corset.
I translate the English version of a leading fashion magazine, so I've also seen photographs of this stuff.
Sounds like you're doing a fun translation.