<p>“performing for” would also be an error if the sentence were punctuated differently:
Ballet, modern dance, and Indian classical dance
[is a form] of theater dance; the dancers, usually
[highly trained] professionals, [performing for]
audiences [in particular] venues and on special
occasions.</p>
<p>As it stands, C is correct. Awkward and poorly written, but technically correct. A is the safe answer, since it’s definitely wrong.</p>