For the croquettes: Put the potatoes in a heavy medium pot and cover with cold water. Stir in the salt and bring to a boil over high heat. Reduce the heat to medium and simmer until very tender, about 30 minutes.
While the potatoes simmer, heat 1 tablespoon of olive oil in heavy large skillet over medium heat. Add the onions and cook until softened, about 4 minutes. Add the garlic and cook until fragrant, about 2 minutes. Add the achiote paste or smoked paprika, if using, mix well until combined, and remove from the heat. Set aside.
Drain the potatoes, cool until able to handle, and peel. Mash them in a large bowl with a fork or potato masher. Add the mozzarella cheese and onion mixture and stir to combine. Season with salt and pepper, to taste. Divide the mixture into 8 balls and flatten them into 3-inch patties.
Heat 2 tablespoons olive oil in a 12-inch nonstick skillet over medium-heat until hot. Fry the croquettes in 2 batches, turning over once, until a crust forms. Drain on paper towels. Carefully transfer the croquettes to a platter. Top with the arugula and drizzle with the remaining 1 tablespoon olive oil. Squeeze lime juice on top and sprinkle with salt and pepper.