Which is the correct usage?
I was surprised that she participated at the performance held at LA.
I was surprised that she participated in the performance held at LA.
You are "in a performance" if you are an actual performer. You are "at a performance" if you are physically there but not in it; for example, a member of the audience. Since she is participating, the correct preposition here would be "in the performance". But a sentence like
changes meaning depending on the preposition.
Participate is normally followed by in, so she participated in the performance is what want you want. (It is conceivable that she participated at the performance might appear in some contexts, but that would mean her involvement was in something other than the performance.)
The key difference is emphasis. In your first example, you are surprised that she participated, then the location is stated. It is not clear that what she is participating in, is the performance. The second is the more obvious meaning, and probably the "correct" one. If she was involved in the performance then it is clear that whatever the location was she was involved.
Perhaps a more clear example:
I was surprised that she danced at the performance last night
I was surprised that she danced in the performance last night
In the first example, we imply that she was dancing, but not as part of the performance. She might have been there to see a band play and felt like dancing.
In the second, we imply that the dancing was part of the show that everyone had come to see. She was part of the performance.