For the Pico de Gallo: 

1. Place the onion in a medium bowl and cover with cold water. Let sit for about 15 minutes. This will help the onion’s intensity to dissipate. Drain the onion and transfer to another medium bowl.
2. Add the cilantro, jalapeño, olive oil, and lime juice to the onion and stir to combine. Season to taste with salt and set aside. 

For the Tacos:

1. Have a medium bowl of cold water ready. Peel the potatoes, cut them into ½-inch cubes, and submerge them in the bowl of water to prevent oxidation from occurring.
2. Warm 2 tablespoons of olive oil in a large cast-iron or heavy bottomed skillet over medium-high heat. Add the chorizo and cook, stirring occasionally until the fat has rendered and the chorizo is crisp, 8 to 10 minutes. Keep the heat on the stove and use a slotted spoon to transfer the chorizo to a plate leaving the oil in the skillet.
3. Drain the potatoes well and add the potatoes to the hot skillet with the reserved oil. Cook over medium-high heat, using a spatula to scrape the bottom of the pan occasionally until the potatoes are cooked through and crisp, about 15 minutes. Transfer the chorizo back to the skillet with the potatoes to warm through. Keep warm in the pan until ready to serve.
4. Warm the tortillas directly over the burners of the stove for about 15 to 30 seconds per tortilla or in a large skillet over high heat, until pliable and slightly charred. Divide the tortillas evenly between 4 plates and spoon some of the potato and chorizo hash over each tortilla.
5. Heat 2 tablespoons of olive oil in a separate large cast-iron skillet or large non-stick skillet over medium-high heat. Crack 4 eggs into the skillet and season to taste with salt and pepper. Cover and cook until the whites are opaque, and the yolks are just set but still slightly runny, 3 to 6 minutes. Transfer the eggs to two plates and repeat this process with more oil, the remaining 4 eggs and salt and pepper. Spoon some of the Pico de Gallo over each taco and serve immediately.