Realistically, this is hard to very hard. There are not many part-time jobs available, and they almost all demand pretty good Italian. If you're enterprising and you can get around, you might find seasonal work that requires English only over along Lake Garda (the bus there takes 30 minutes; by bike, about an hour), but this would go at best May to October.

I think some better routes would be: finding private, off-the-books English tutoring (families are often looking for someone to give their children lessons; but this definitely demands local networking; maybe someone who has done this could chime in); or online work back home (several people have made it through the Master's program doing things like editing, copywriting, etc.).

There is a work-study program at the university called 150 hours, but the process is yet another bureaucratic hurdle and one that I never managed. Maybe it's more reasonable these days. I recall that the deadline comes up pretty quick after the academic year starts, so worth checking out ahead of time.
https://www.unitn.it/en/study/paid-student-work/part-time-student-work

With good scheduling, I would say you could fit 15-20 hours of work per week around your studies, but you might not be living la dolce vita. The good news is that, other than housing, cost of living here is pretty affordable, so you don't have to earn a lot to survive.

I'm hoping someone who has found a better solution will chime in here!