Obviously it helps if you have some knowledge of Greek mythology and if you have chosen a specific topic, then you will need to research those aspects of Greek mythology related to your topic. But otherwise, the key ingredients of a successful research paper are the same regardless of the topic. You need to have the following characteristics.
The main focus of the research paper is that it provides factual information. In your thesis statement you will set out your goal for creating this research paper and any reader must be able to measure whether or not you have achieved your goal. Unless the reader is able to test your statements, to measure them, you will receive a low mark.
The topic of your research paper will be specific and will be complemented by the specific information and facts you provide in your writing. There is no room in a research paper for personal opinion or any information which is not grounded in solid evidence. Even when writing about a mythical subject, specific facts are essential.
Objectivity will always be relevant when writing a research paper. If you do choose to give an opinion then you must be able to substantiate what you have stated. Anyone writing a research paper who takes a subjective approach to the topic is opening themselves up to failure.
A research paper will never contain personal musing on whatever the topic is being discussed. It must be specific. It must be detailed. It must be precise. This is not an opinion piece but a report of what facts have been discovered thanks to proper research.
The whole point of a research paper is that it homes in on a specific topic and the information provided in the introduction, the fact paragraphs and the conclusion must all relate to the title of the document. It is a total project with each section adding to the whole effect.
There is no substitute for solid research in creating a research paper. Greek mythology is widely covered in many sources and information is freely available.