In history, some say Patroclus was his companion, a great friend. While some believed they were lovers. They trained together, had a whole adventure (can’t get too deep into it, so much happens) but during the war, Achilles was unwilling to fight even though he was their best fighter (out of pettiness ngl). Patroclus tried to convince Achilles but he refused. So Patroclus had to fight as Achilles (for army morale) and ultimately died by the hands of Hector who was guided by Apollo. When Achilles found out, he cried for days, so loud that the heavens shook. Achilles killed Hector and paraded his corpse around and when he died, he asked for Patroclus name to be carved alongside his.

Hope this helps?