MAKE THE CILANTRO MARINADE: For the marinade, in a blender or food processor, combine the cilantro, pepper, salt, olive oil, lime juice, lemon juice, and garlic. Cover and blend or process until smooth. Place the chicken breasts in 2 large resealable plastic bags; add half of the marinade to each bag. Marinate in the refrigerator at least 1 hour but no more than 2 hours.
MAKE THE GUACAMOLE: Meanwhile, scoop the avocado flesh into a medium bowl. Mash with a fork. Stir in the tomato, onion, garlic powder, salt, pepper, and lime juice. Cover and refrigerate until ready to serve.
MAKE THE CHICKEN AND SHRIMP: Preheat the grill to high. Remove the chicken from the marinade; discard the marinade. Arrange the chicken on a grill rack. Grill, turning once halfway through, until cooked ( 165°F ), 14 to 15 minutes.
MEANWHILE, place the shrimp in a large bowl. Drizzle the lime juice over the shrimp and toss to coat. Sprinkle the Tajín seasoning over the shrimp and toss to coat.
TRANSFER the chicken to a large platter; tent with foil to keep warm. Add the shrimp to the grill. Cook, turning once halfway through, until trans- lucent and pink, 2 to 3 minutes.
SERVE the chicken with the shrimp and guacamole. Top with cilantro and serve with lime wedges.
*Tajín seasoning is a shortcut to great flavor in this recipe. It’s a popular seasoning blend in Mexico and is often sprinkled on mango or melon. The only ingredients are dried and ground chiles, salt, and dehydrated lime juice—so it’s totally compatible.