His first translation of Homer's work came in 1598, Seven Books of the Iliads of Homer, and was dedicated to Robert Devereux, a favorite of Queen Elizabeth, in hopes of finding a wealthy patron. He finally found a patron in James I's son and heir, Prince Henry. Henry died in 1612 at the age of eighteen and Chapman persevered, although poor, in his translation of Homer. He published The Whole Works of Homer in 1616, having translated The Odyssey along with The Iliad. It took him almost thirty years to accomplish this feat, armed with a Greek to Latin dictionary and a Latin version of Homer alongside a Greek text. It is not certain how much education he had in Greek but, if he was untrained, his determination and accomplishment is inspirational.
Greek philosophers in the Middle Ages were not 'lost' because the texts were all lost but because people lacked the ability to read them and few translations were available. Boethius was one of the last few in the West who could read Greek. Heloise was distinguished by her ability to read Greek. Not only could she read Latin and Greek but she also knew some Hebrew. That she could read Latin was astonishing enough for a woman of her time but to know Greek and Hebrew as well made her singular even for a man. Abelard knew only a little Greek and no Hebrew.
What little was known of Plato during most of the Middle Ages was the translation of Timaeus by Calcidius. It might be worth looking at this text. Before there was 'The Force' (Star Wars), there was Plato's view of a 'World Soul'. The Timaeus lay at the heart of Boethius' ninth meter in his third book, the very center of Consolatio Philosophiae.
I sometimes think about Chapman laboring, struggling with a difficult language to write a book that no one had asked him to write and few would know or care that he wrote. It was not a literal translation, few at that time did literal translations. He was accused of merely translating the Latin text and those critics he called 'envious wind fuckers'. He died in poverty in 1634. You can still buy his version of The Iliad.
I have a 2003 edition published by Wordsworth Classics which includes an introduction on Chapman by Dr. Adam Roberts.