Bloom the aromatics: Set Instant Pot to Sauté. Warm oil, then cook onion and garlic 2–3 min until softened. Stir in chili powder, cumin, and paprika; let spices toast 30 sec.
Build the soup base: Add chicken breasts, diced tomatoes + chiles, broth, oregano, and a pinch of salt. Secure lid, set valve to Sealing, and cook on Manual / High Pressure — 12 min. Allow a 5-min natural release, then quick-release any remaining pressure.
Shred & finish: Transfer cooked chicken to a plate; shred with two forks. Return meat to pot, add zucchini ribbons and lime juice, and switch back to Sauté for 2 min — just until the “noodles” soften. Taste; adjust salt, pepper, or lime.
Serve: Ladle into bowls and top with avocado, cilantro, extra lime, or your favorite low-carb garnishes.