After Hector's death, King Priam told Memnon to fight Achilles.
In result of the duel, Achilles killed Memnon.
Paris in rage, wanted to give payback to Achilles for killing his brother hector and friend Memnon. Paris shot an arrow, and as strong as he stretched the arrow it started to die down and fall to the ground, but hit Achilles heel.
Once the arrow hit Achilles heel, Achilles was trying to get up and fight and Paris, suddenly Paris shot Achilles in the chest and Achilles died.
When the Greeks saw Achilles die they suddenly retreated. But, when all seemed lost Athena proposed an idea and they took it.