Hachiman is a teenage boy with short black hair, and is most prominent feature is his set of "dead fish-eyes" and a strand of hair sticking upwards. He is always seen wearing his school uniform and a casual orange T-shirt.
Hachiman more than once mentions that he has a handsome face, to which Yukino retaliates by saying that he has rotten eyes, without commenting anything about supposed "handsomeness".
In the light novel, Yukino states that she criticized Hachiman's unattractive facial expression, not his facial features, which she believes to be the proof of his twisted nature. Once Yui answered to Totsuka, who felt that Hachiman is outstanding by saying that he is so plain-looking and it would take quite a lot to notice a person like him.
From both their description, it is not too far-fetched too assume that if not for his sullen expression and his "dead fish-eyes" (rotten eyes), he can be considered handsome.
In anime version, whenever Hachiman's past are shown, it should be noted that his eyes was covered by shadow or his eyes were purposely never shown to audience.