Dina,横线 for months to find a job as a waitress,finally took a

答案是 C.having struggled
这个句型叫 Perfect Participle （完成式分词）
这是固定的句型.
having struggled for months to find a job as a waitress
after having struggled for months to find a job as a waitress
after struggling for months to find a job as a waitress
上面三个句子有相同意思
现在分词的完成式表示其动作在谓语动词的动作之前已完成.
例句：
Having finished her homework,the little girl began to watch TV.
做完作业后,这个小女孩开始看电视.
Having lived in Beijing for many years,Carter knew the city well.
（因为）在北京住了多年,卡特对这个城市很熟悉.
百度对这个句型有详细解释：为什么用这句型句子的意思是迪娜，在挣扎了几个月仍旧找不到一份饭店服务员的工作之后，终于接受被聘为附近的一家广告公司的职员。上面指出现在分词的完成式表示其动作在谓语动词的动作之前已完成从语境我们知道迪娜“找一份饭店服务员的工作”这件事已结束，所以用现在分词是对的。