Place chicken breasts in a large pot or Dutch oven, cover with water, and bring to a boil. Reduce heat and simmer for 15-20 minutes, or until cooked through. Remove chicken from pot, reserving 0.5 cup of cooking liquid. Shred chicken using two forks and set aside.

While chicken cooks, prepare the sauce. Heat 1 tablespoon of olive oil in a large skillet over medium heat. Add the sliced half of the yellow onion and cook until softened, about 5-7 minutes. Add garlic and cook for 1 minute more until fragrant. Remove from heat.

In a blender, combine the cooked onion and garlic, roughly chopped half of the yellow onion, chipotle peppers, adobo sauce, diced tomatoes, chicken broth, cumin, oregano, salt, and pepper. Blend until smooth.

Heat the remaining 1 tablespoon of olive oil in the same skillet over medium heat. Pour in the blended sauce and bring to a simmer. Add the shredded chicken and stir to combine, ensuring all chicken is coated. If the sauce is too thick, add a little of the reserved chicken cooking liquid. Simmer for 10-15 minutes, allowing the flavors to meld.

Warm the corn tortillas according to package directions (on a dry skillet, microwave, or wrapped in foil in the oven).

Fill each warm tortilla with a generous amount of chicken tinga. Top with chopped cilantro, diced red onion, sliced avocado, and a drizzle of Mexican crema. Serve immediately with lime wedges.