They were stuck in a tough situation so priam sent a letter to Memnon saying that he needed help.
Memnon arrived and challenged anyone that thought they could beat him. Knowing that he was one of the strongest warrirors of the land.
This shows Achilles on his way to fight memnon after hearing that he was challenging anyone brave enough to fight him. He was thirsty for Memnon's blood, since he killed king Nestor's son which was one of Achilles friends.
Achilles ends up winning the fight against memnon, which was a worthy opponent to Achilles. He stopped moving and raised his hand in triumph. Paris saw this as an opportunity
The god Apollo was looking down from mount olympus. Angry that Achilles was victorious so he helped guide Paris's arrow to the only place that Achilles wasnt dipped in the river of immortality