He was in an area (nearer the lighthouse) that he didn't usually go to, looking for pearls and suchlike while Nemuri hunted in a different area. There is a group of sailors who go out on their lobster boat around the lighthouse, drunk, hunting for mermaids. Aizawa usually wards them off since they're not allowed to fish in those waters as it's his property.
Anyway, they see what they suspect to be a mermaid tail whipping around under the waves, and shoot a harpoon at it, but it soon disappears further into the water. Aizawa hears them shouting and rows out to tell them to go home which they eventually do.
Hizashi can't swim with the harpoon in his tail and he's losing a lot of blood so he ends up washed up on the beach of the island, and stays there overnight in the freezing cold, drying out, until Aizawa finds him.
Nemuri doesn't know what happened to him until they meet up again, although he calls out to her from the lighthouse (merpeople can communicate by wailing/'singing' and you Know he's loud) so she knows he's at least alive.