In a blender, puree cilantro, water, lime juice, garlic, salt and pepper until smooth. Place fish on a rimmed plate and pour marinade over, turning to coat. Let sit 5 minutes.
To prepare the sauce, in a blender, puree olive oil, bitter orange juice, cilantro, parsley, chives, salt and a pinch of pepper until smooth. Pour into a small saucepan and place over medium-high heat. When sauce starts to boil, add broth and season to taste with salt and pepper.
Heat oil in a skillet over medium high heat. Sear fish filets until golden and cooked through, about 2-3 minutes per side. Transfer to plates and spoon over warm green sauce to serve.