The Greek Agamemnon of Mycenae was a conqueror who wanted to gain more lands and gain more Glory. His brother Menelaus was less of a Conqueror and more of a ruler.
Prince Hector of Tory and his brother Paris made a peace treaty with Menelaus , the King of Sparta and Agamemnon's brother.
Achilles was a fierce Greek warrior who wanted his name to live after he dies. He mentioned the idea of 'being remembered after death' many times during the movie and it was obvious that this what was he really wanted. See also why people love the Movie Troy.
Paris , who was having an affair with Menelaus' wife Helen, smuggled her into their Trojan ship. Hector got furious when he knew what his brother did. It was late to take Helen back and so the ship had to sail back to troy.
When Menelaus found that his wife ran away he became furious and went to Agamemnon to help him get revenge against the Trojans. Agamemnon was so glad because this gave him an opportunity to conquer another city especially that he already wanted to Conquer Troy since a long time.
Achilles , who hates Agamemnon, was hesitant to join the war but his mother convinced him that if he went to Troy his name will get remembered for centuries so he made his mind and sailed with Agamemnon's army.
The Greek's arrived with their large army to the beach of Troy and easily conquered it with the help of Achilles and his Myrmidons.
Paris decided to have a 1-on-1 fight with Menelaus to save the city. Agamemnon had plans to conquer Troy anyway. Menelaus almost killed Paris but Hector rushed in and killed Menelaus. Agamemnon ordered the army to attack Troy.
Hector killed Achilles' cousin by mistake thinking that he was Achilles. Achilles became furious and went to the Trojan walls to challenge Hector for a fight. Hector accepted but he was killed by Achilles during the fight.
The Greeks hid their ships and left a large wooden horse to the Trojans (a gift). The Trojans thought that the Greek army left. They took the horse inside then in the night Greek soldiers , who were hiding inside the horse, opened the gates for the rest of the army and the city was sacked.
According to the Greek legend Achilles' weak point was his heels. Paris shot Achilles in his heel during the fight then kept shooting arrows at him until he died. During the fight Agamemnon , Priam and Glaucus were killed.
After troy fell funerals were held for the slain. The narrator talked about men such as Hector and Achilles who died but still lived because of the great deeds they did in their lives. The song 'Remember me' by Josh Groban was then played. See Interstellar Movie explained.