Soak the dried corn husks in warm water for at least 30 minutes until pliable. Drain and pat dry before using.
In a medium pot, combine the chicken breasts, quartered onion, and garlic cloves. Cover with water and bring to a boil. Reduce heat and simmer for 30 minutes or until chicken is cooked through.
Remove the chicken from the broth and let cool. Reserve 2 1/2 cups of the broth for the masa dough.
Shred the cooled chicken into bite-sized pieces using two forks.
In a dry skillet over medium heat, toast the guajillo and ancho chiles for 1-2 minutes until fragrant, being careful not to burn them.
Place the toasted chiles in a bowl and cover with hot water. Let soak for 15 minutes until softened.
Drain the chiles and transfer to a blender. Add cumin, oregano, black pepper, salt, and 1/2 cup water. Blend until smooth to make the red chile sauce.
In a bowl, mix the shredded chicken with the red chile sauce until well combined. Set aside.
In a large mixing bowl, combine masa harina, baking powder, and salt. Gradually add the reserved chicken broth while stirring until a soft dough forms.
In a separate bowl, beat the softened lard with vegetable oil until fluffy.
Add the lard mixture to the masa dough and beat with an electric mixer or by hand until the dough is light and fluffy. The dough should be spreadable but hold its shape.
To assemble the tamales, spread about 2 tablespoons of masa dough onto the center of a soaked corn husk, forming a rectangle about 4×3 inches.
Place 1-2 tablespoons of the chicken and chile filling in the center of the masa.
Fold the sides of the husk inward to enclose the filling, then fold the bottom up and the top down to seal the tamale.
Repeat with remaining husks, masa, and filling.
Place a steamer basket in a large pot and add water below the basket level. Arrange the tamales standing upright in the basket.
Cover the pot with a lid and steam the tamales over medium heat for 1 to 1 1/2 hours, checking occasionally to ensure water does not evaporate. Add more water as needed.
The tamales are done when the masa separates easily from the husks.
Remove tamales from the steamer and let cool for 5 minutes before serving.