In a medium saucepan, bring 2 cups of water to a boil. Add the guajillo and ancho peppers and simmer for about 10 minutes until softened. Drain and set aside.
In a blender, combine the softened peppers, onion, garlic, chicken broth, diced tomatoes, apple cider vinegar, cumin, oregano, smoked paprika, salt, and black pepper. Blend until smooth.
In a large pot or Dutch oven, add the chicken thighs and pour the blended sauce over them. Bring to a simmer over medium heat, then cover and cook for about 30-40 minutes, or until the chicken is tender and fully cooked.
Remove the chicken from the pot and shred it using two forks. Return the shredded chicken to the pot and stir to combine with the sauce.
Heat a skillet over medium heat. Lightly toast each corn tortilla for about 30 seconds on each side until warm and pliable.
To assemble the tacos, place a generous amount of the chicken mixture on each tortilla. Top with chopped cilantro and a squeeze of lime juice.
Serve immediately with extra lime wedges on the side.