A pastime is something done to occupy time. It is an agreeable thing to be done. It therefore is not the answer.
A pursuit is more serious. It is an activity that is meant to find an answer, one that may evade one for a long period of time. But a pursuit is not a disagreeable activity; it is one done willingly. A pursuit is not the answer.
An activity is a neutral word. It is anything that is done. In itself is not anything either agreeable or disagreeable.
Chore is the word I would pick. That is a job that must be done. It suggests repetitiveness. It does not have to be agreeable. I'd pick this one. The dictionary says that it can be a disagreeable task.
Pastime doesn't really have a negative connotation basically means how things agree. Pursuit doesn't either neither does activity. Maybe chore? Kids usually use chores as a way of saying they're being forced to do something they don't want to do. Pretty sure it's the only answer that actually makes sense.
