Combine all of the marinade ingredients in a blender until smooth.
Cover the shrimp in the marinade in a bowl or zip-top bag and marinate in the fridge overnight, or for at least 4 hours.
Preheat the oven to 350°F. Arrange the shrimp on a baking sheet, discarding the marinade. Roast for 6-8 minutes, until cooked through and bright pink.
Meanwhile, make the quinoa by combining the quinoa with 4 cups of water and a pinch of salt in a medium saucepan. Bring to a simmer, reduce heat to low, cover and cook until the grains are tender, about 12 minutes. Fluff the quinoa with a fork, then stir in the cilantro, scallion, lime juice, olive oil, salt and pepper to taste.
To make the relish, combine all of the ingredients in a bowl and let sit for 10 minutes.
To make the black beans, heat the oil in a large skillet over medium-low heat. Add the garlic and cook, stirring, until fragrant, about 1 minute. Add the black beans, cumin and salt and remove from the heat.
To make the lime vinaigrette, add all of the ingredients except the oil to a bowl and whisk well or purée with an immersion blender. While whisking/blending, drizzle in the oil until emulsified. Season to taste.
To serve, divide the lettuce and quinoa between bowls. Top with achiote shrimp, black bean salad, tomato onion relish, and drizzle with lime vinaigrette. Sprinkle with cotija cheese and serve with tortilla chips on the side.