You are right: you are headed for a lot of one day/two night stops, a very rushed trip.
Fly into Venice & out of Milan to save some time. I am going to assume you have 13 nights. Is that right? You do not mention your interests, which could also skew advice. And is this your first trip to Italy? OK, with lots of assumptions and guessing:
Venice - 3 nights is perfect
Verona - What do you want to see here? Personally I am not a fan but many are. Before devoting nights to it, make sure you know what you want to see. OR Leave Venice early, stop here for 5 or 6 hours then continue on to Florence.
Florence - 3 nights for a highlight tour. See a couple of the major museums. Have a plan because advance reservations are advisable for some sites.
Cinque Terre - 3 nights. Assume you like the outdoors and maybe hiking? Boat to PortoVenere is nice, too.
Lago di Como (suggest Varenna) - 3 nights for relaxing, cruising the lake.
OK, you may have one night left with my plan. Obviously Parma has to go. You could spend a night in Verona, or spend your final pre-flight night in Milan. Or add a night to Florence! If you have a late enough flight from Milan you can chance coming in from Lago di Como the morning of departure, but check transit options and travel times carefully.