A short, simple list:
Blender - a high-speed blender gives you the smoothest result, but any reasonably powerful blender works for this recipe since the goal is a thick, spoonable consistency rather than a perfectly silky drink.
Measuring cups and spoons - for the berry mix, banana, nut butter, and liquid.
Serving bowls - wide and shallow, which lets you arrange toppings attractively across the surface rather than having them sink into a deep glass.
Spatula - for scraping the thick smoothie mixture out of the blender, since this consistency is much thicker than a drinkable smoothie and won't pour out easily on its own.
That covers the complete equipment list. A blender and a couple of bowls handle the entire recipe.