A heroine is a female hero, so hero is the best synonym here.  

None of the other answer choices work.  Not all females are heroines, so that answer choice does not work.  Similarly, heroines can be young or old, so adolescent is incorrect.  Someone can also be an adventurer without being a hero.  Lastly, anthropologists study humans, which has nothing to do with heroines.

A "nemesis" is an opponent or rival, a person or group with which you are especially competitive. For example, pretend that your school football team often plays against another team. You and your friends get excited for those games, especially hate when your team loses, and might even talk about the opposing team members as enemies. The opposing team would be your nemesis. Of the other choices, an "acquaintance" is someone that you know, a "relative" is a family member or someone to whom you are related, and a "namesake" is a thing that shares its name with something else, or is directly named after it.

A "journalist" is a person who researches and writes news stories, or a "reporter." A "professor" is a person who teaches at a university or college. A "dentist" is a medical professional who cleans and operates on teeth. An "accountant" is a person who states and reviews the financial statements of a person or company. A "principal" is the person in charge at a school.

An "entourage" is a group of attendants. The best choice is "attendants," because it is a part of the definition of "entourage."

A felon is someone who has committed a crime. To further help you, a politician is someone who is involved in government; a miser is someone who hates spending money and tries to save as much as possible.

"Nemesis" is a noun that refers to a long-standing rival. Of the answer choices, the word with the closest meaning is "enemy," which means rival or nemesis.  "Feud" refers to a prolonged dispute; "diagnosis" means the act of classifying a problem or illness; and a "sonnet" is a poem made up of fourteen lines.

A "recluse" is a person who lives apart from society. The best choice is "hermit" because it has the same definition as "recluse." 

Your “nemesis” is your enemy, so "enemy" is the correct answer. To provide further help, an “ally” is someone who is on your side or a friend, an “accomplice” is someone who works with you, usually on a risky or nefarious mission, “protagonist” means hero, and “antagonist” means villain. “Nemesis” is an antonym of “ally” and “accomplice.” Likewise, “protagonist” is an antonym of “antagonist.”

A “rascal” is someone prone to bad behavior, a scoundrel. To provide further help, a “contributor” is someone who helps something get done; a “politician” is someone tasked with making laws and governing; a “principle” is a guiding standard of belief or morals; “rakish” means charming and dashing. 

A "colleague" is a coworker or someone a person works with, so "coworker" is the correct answer. An "autobiography" is a book written by someone about that person's own life. "Assignment" means task or work given to a specific person. An "author" is a person who writes a story, novel, or other book. "Task" means piece of work that needs to be completed.