Which pronoun best completes the sentence?
each dancer gave the performance all.

Well, it's asking for pronouns. 

your options are: Me, you, him, her, it, us, them, our, ours, your, yours, his, hers, its, theirs, their

you are talking about dancers here, so you can get rid of all the first-person and second-person ones, as well as the plural ones, because the subject is "dancer."
This leaves you with: his, it, and her. "It" doesn't make sense at all. My first instinct as a dancer myself is to say "her", since most dancers are female. However, the sentence doesn't specify gender, and even one male in a whole class of female would make this "his". And, who knows? It could be a guy dance class. therefore, the safe answer is "his", although your teacher will likely take "her" as well for an answer