Lucky Dags is a single-target enemy, which makes it very easy when on its own. However, it compensates for this with very high damage and a rapid attack rate, meaning that any cat that gets hit is a lost cause. It is particularly dangerous when stacked, like in Sins and Blessings, where the many Lucky Dagses attack faster than one can spam cats.
Make sure to spam meatshields at all times. You can prioritize the cheaper ones because Lucky Dags can instantly kill most units. Using high DPS units is a good idea, because Lucky Dags can't hit them even if they are in its range. Fast units such as Valkyrie may not work when there are multiple of them, because immediately after the first group of meatshields die, Valkyrie charges ahead of the second group, getting killed instantly.