Season the fish with ½ teaspoon salt and ¼ teaspoon pepper. Place in a large skillet with enough water to reach halfway up the sides of the fish.
Bring to a simmer over medium heat. Cook the fish, covered, until opaque throughout, 6 to 8 minutes.
Transfer the fish to a plate and refrigerate until cool, about 15 minutes. Using a fork, flake the fish into large pieces.
Meanwhile, in a large bowl, whisk together the oil, lemon juice, mustard, cilantro, ½ teaspoon salt, and ⅛ teaspoon pepper.
Toss the dressing with the mixed greens, chickpeas, avocado, and onion. Divide among plates and top with the fish.