It shouldn't be surmised from the above phrase that Achilles was gay, because he was also banging Brisseis.
In any case he was bi.
Ajax: Achilles, Hector wasted your boyfriend Patroclus, who was wearing your armor and a red garter belt. Now Hector has both your armor and the garter belt.
Achilles: What?? I told him countless times that only black garter belts are worn with armor!
Im gonna beat the shit outta that Hector dude as soon as I finish banging Brisseis.
A tall, frosty, beverage!
Mmmmm! Nothing like a good patroclus after a long day!
Go get your own Patroclus, You tall-frosty-beverage stealer!