According to the rules of Russian grammar after "достичь" we should use only the object in genitive case. So the correct variant is "достигла своЕЙ основнОЙ целИ"
"дорогого плода ее матки" - IMHO it`s too literal translation. In translating an artistic text, we can well use method called "Full rearrangement" to to achieve euphony.