This Exekias black-figure design dates to around 530 BCE.
The story depicted here, quite a common one in Greek art, shows Achilles killing the Amazon Queen, Penthesileia. As the fatal blow is delivered, however, their eyes lock and, as maybe you've guessed already, they instantly fall in love. And she dies. It is one of the many scenes in Achilles' life that Homer wisely decides to omit.
Note how black and murderous Achilles seems, quite rightly, to be. His helmet is down, shielding his face. Her face, however, is exposed. Amazons were, for the Greeks, awkward monsters. They represented the uncivilized, perverse, un-Greek extreme. Note the Amazon's white skin tone here, traditionally used for women to indicate they spent time indoors; it seems odd here, though does emphasize her delicate nature and underscores the brutality of the act. As violent as the scene is, however, it is also a posed scene. Achilles lumbers up somewhat stiffly, and Penthesileia strikes a theatrical pose. It is as if they are rehearsing the scene.
I don't know what to make of the swirling lines around them.