Break down the chicken into 6 parts--2 thighs, 2 breasts, and 2 wings.
Add the chicken pieces to large bowl with the Worcestershire sauce, 2 tablespoons of canola oil, the salt, and pepper and toss to coat.
In a large pan over medium-high heat, add the chicken, skin-side down, and the remaining tablespoon of oil. Sear the chicken until browned on both sides and the skin is crispy, about 5-8 minutes per side. Remove the chicken from the pan and set aside.
To the hot pan, add the onion, celery, green chiles, garlic, and tomato paste, stirring to combine after each ingredient is added. Sweat until fragrant and the onions are translucent, about 5 minutes.
Deglaze the pan with the beer and chicken stock. Return the chicken to pan, cover, reduce the heat to medium-low, and braise for 1 hour.
Make the pico de gallo: In a large bowl, combine the tomatoes, onions, jalapeño, salt, cilantro, and the lime zest and juice. Stir to combine.
Make the avocado yogurt: In a large bowl, combine the yogurt, avocados, lemon juice, salt, pepper, and olive oil. Mash with 2 forks until mostly smooth and well combined.
Preheat the oven to 350˚F (180˚C).
Remove the chicken from the braising liquid. Increase the heat to high and cook the braising liquid until reduced by half, about 30 minutes.
Using forks, shred the chicken and place the meat in a large bowl. Discard the bones or save for another use.
Add 1 cup (240 ML) of the reduced braising liquid to the chicken and stir to combine.
Assemble the nachos: Spread the plantain chips on a baking sheet in an even layer. Top with half of the black beans and all of the chicken, then the remaining black beans. Cover with the cheddar, mozzarella, and pepper Jack cheeses and finish with the pickled jalapeños.
Bake for 10-15 minutes, or until the cheese is melted.
Top the nachos with the pico de gallo, avocado yogurt, and cilantro.