Place the chicken breasts in the Instant Pot inner pot in a single layer.
In a small bowl, whisk together the ancho chili powder, ground cumin, ground coriander, and 1/4 tsp salt and 1/4 tsp black pepper.
Sprinkle the spice mixture evenly over both sides of the chicken, then scatter the minced garlic over the top.
Pour the fire-roasted salsa over the chicken to mostly cover it.
For Instant Pot: Close the lid, set the valve to sealing, and cook on Poultry or Manual high pressure for 13 minutes, then use quick release according to the manufacturer's instructions.
For slow cooker: Cook on low for 5–6 hours until the chicken is tender and shreds easily.
Remove the chicken to a cutting board and let it rest a few minutes, then shred with forks or shredding claws.
Return the shredded chicken to the pot with the cooking juices, add the chopped cilantro, and toss to coat; taste and add more salt if needed.
Use tongs to transfer drained chicken to warmed tortillas and top with cheese, romaine, diced tomatoes, guacamole or avocado, and sour cream and hot sauce if desired.
