Season the chicken: Pat the chicken dry. Sprinkle with salt, pepper, cumin, chili powder, smoked paprika, and oregano.
Rub to coat evenly.
Stovetop method: Warm olive oil in a large skillet or Dutch oven over medium heat. Add onions and cook until softened, 3–4 minutes. Stir in garlic for 30 seconds.
Nestle in the chicken and pour the salsa over the top. Bring to a gentle simmer, then cover and cook on low for 15–20 minutes, flipping once, until the chicken reaches 165°F.
Slow cooker method: Add onions, chicken, spices, garlic, and salsa to the slow cooker. Cook on Low for 4–5 hours or High for 2–3 hours, until tender.
Instant Pot method: Add onions, chicken, spices, garlic, and salsa to the pot.
Seal and cook on Manual/High for 10 minutes (12 minutes for thick breasts). Quick-release pressure after 5 minutes of natural release.
Shred the chicken: Transfer chicken to a cutting board and shred with two forks. Return it to the pot, toss in the salsa juices, and simmer uncovered for 3–5 minutes to thicken if needed.
Brighten it up: Stir in the lime juice and taste.
Add more salt or a pinch of sugar if your salsa is very tangy.
Warm the tortillas: Toast tortillas in a dry skillet for 30–60 seconds per side, or wrap in a damp paper towel and microwave until pliable. Keep warm in a clean towel.
Assemble the tacos: Fill tortillas with shredded salsa chicken. Top with cilantro, cabbage, onion, avocado, jalapeños, a squeeze of lime, and any other favorites.