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, as groups of Lucky Dagses can attack faster than one can spam cats.
Strategy[]
Make sure to spam meatshields at all times. You can prioritize the cheaper ones because Lucky Dags can instantly kill most meatshields other than high leveled Eraser Cat or Manic Eraser Cat. Using units with high DPS like Ring Girl Cat is a good idea, because Lucky Dags can't hit them even if they are in its range. Fast units such as Valkyrie Cat may not work when there are multiple of them, because immediately after the first group of meatshields die, Valkyrie Cat charges ahead of the second group, getting killed instantly.
Turn the animation on and off using the switch in the upper left. Clicking the viewer background enables scrolling and zooming with the mouse if on desktop. Note that browser zoom may cause issues with scrolling and zooming. A list of available backgrounds can be found here. For more info on usage, see here.