Remove the skin from the chicken by gripping it firmly and pulling it back from the meat. It should come off the thighs easily. For drumsticks, hold the thick end and pull the skin down toward the bone, then use a knife or kitchen shears to cut where it's attached at the bone. Discard the skin.
Clean and tenderize the chicken by placing it in a large bowl, adding vinegar, lime juice, and enough cold water to cover the chicken. Let soak for 15 minutes, then drain and rinse thoroughly. Pat the chicken dry with paper towels.
Season the chicken with sofrito, sazón, soy sauce, adobo, oregano and cumin. Toss until coated evenly, then cover the bowl with plastic wrap and let the chicken marinate in the refrigerator for at least 1 hour, or overnight.
Heat the oil and sugar in a heavy-bottomed pan, over medium heat. Stir occasionally, letting the sugar caramelize (the oil will start to turn brown).
Brown the chicken in batches, starting with drumsticks and flipping as needed. Be careful not to crowd the pan, because the chicken won't brown as nicely. Once brown on all sides, transfer the drumsticks to a plate and repeat this process with the thighs.
Set the chicken thighs aside with the drumsticks. Make sure to keep the drippings left in the pan. Use a large or wooden spoon to start to loosen the bits stuck to the bottom; these bits adds flavor to the sauce.
Make the sauce by adding ½ cup of water to pan along with any juices left over from seasoning the chicken. Over medium heat, continue loosening the bits from the pan using a spoon. Add the tomato paste and bouillon, stirring until the sauce is smooth and dark in color.
Braise the chicken by putting it back in the pan with 1 additional cup of water, or just enough to cover it. Bring to a simmer, then cover and let it cook in the sauce for 30 minutes. Stir occasionally—flipping the chicken as needed, making sure the sauce doesn't dry out or burn. Add a few splashes of water if the liquid level gets too low.
Add the peppers, onions and olives, topping off with a little water if needed, then cover and let simmer 5-10 minutes more, until they're tender but still slightly firm. Let sit for a few minutes before serving.