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Combine chicken, tomatillos, poblano peppers, Anaheim peppers, Serrano peppers, onion, garlic, cumin, and a big pinch of salt in a pressure cooker. Heat over high heat until gently sizzling, then seal pressure cooker, bring to high pressure, and cook for 15 minutes. Release pressure.
Using tongs, transfer chicken pieces to a bowl and set aside. Add cilantro and fish sauce to remaining contents of pressure cooker. Blend with a hand blender or in a standing blender and season to taste with salt. Return chicken to sauce, discarding skin and bones and shredding if desired. Transfer to a serving platter, garnish with chopped cilantro, and serve immediately with tortillas and lime wedges.