The sentence is quite complex. Therefore, you should start from breaking it down into smaller chunks.
1. She was less successful after she had emigrated to New York (questions: who is SHE? less successful compared to WHEN? are the tenses used correctly?)
2. compared to her native Germany - it seems that we are comparing a clause "she was less successful" to a phrase "her native Germany"; also it is incorrect to use "compared to" AND an expression showing contrast ("LESS successful")
3. photographer Lotte Jacobi nevertheless earned a small group of discerning admirers (we need to check whether the underlined part matches the non-underlined part grammatically and stylistically).

The pronoun "she" is used correctly with reference to Lotte but the original sentence compares a clause to a phrase. Answers B and D repeat the same mistake and can be eliminated. We are left with C and E.
Answer C is correct. The sentence uses past tenses correctly to indicate the sequence of events.
Answer E is incorrect because it uses the Past Perfect to talk about an action in the past that happened after and not BEFORE another one. Secondly, sentence E is a run-on. It lacks a conjunction between the first two clauses that would make the structure logical.