Slugging is a way of saying fighting (in American English, to punch someone is to "slug" them). If that was the meaning, they're saying that you both had to fight (work) very hard, for the duration of the event or time period. A constant challenge.
It could also be that they meant "slog", which is more of a British term for a long, difficult walk. A similar meaning, but this one would suggest more of a boring, exhausting and unending task.