Combine chicken, poblano peppers, tomatillos, onion, Anaheim peppers, Serrano peppers, 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 an immersion blender or in a countertop 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.
