Your answer would be that the compund predicate is "fulfilled her dreams and became an English teacher".
Explanation:
A compound predicate is two or more verb phrases that share the same subject and are joined by a conjunction. In order to identify a compound predicate in a sentence, you should ask yourself what the subject does or is. The answer to that question is the compound predicate. What did she do? (She) fulfilled her dreams and became an English teacher.
