slog away
To work (on something) strenuously and continuously, especially for a long period of time. Sorry, I won't join you for lunch today—I've got too much to do, so I'm just going to keep slogging away. I've been slogging away at this report for the last three days. I'm just ready for it to be finished!
slog away
v. To work diligently for a lengthy period of time: The student slogged away on the algebra assignment.