First, place your beef short ribs in a large pot and add enough water to cover the meat. Bring this to a boil over medium-high heat. As it boils, you'll see gray foam rising to the top - remove this with a spoon to get a clear broth.
When the broth looks clear, add your quartered onions, tomatoes, and fish sauce. Lower the heat to a gentle simmer, cover the pot, and cook for about 1 to 1½ hours. You'll know the meat is ready when it easily pulls away from the bone. Add more water occasionally if needed to keep the meat covered.
Once the meat is tender, add the peeled and halved taro. Let these cook for about 7 minutes until they start to soften. Add your finger chilies (keep them whole for mild heat or cut them for more spiciness) and the sliced radish. Let these cook for another 5 minutes.
While waiting, prepare your kangkong by cutting off the tough bottom ends and separating the stalks from the leaves. Now add your sinigang mix powder to the pot and stir until it dissolves completely. Taste the soup and add salt and pepper as needed.
Add the kangkong stalks first and cook for a minute. Then add the leaves and cook just until they turn bright green and slightly wilted, about another minute. Don't overcook the leaves or they'll become too soft.
If you're using fresh tamarind instead of powder, prepare it while the meat is cooking. Boil the tamarind in a cup of water until soft, mash it well with a fork, then strain the liquid to remove seeds and pulp. Add this to your soup until it's as sour as you like.
Turn off the heat as soon as the kangkong leaves are wilted. Serve your sinigang hot in bowls, with steaming white rice on the side. For extra flavor, serve with a small dish of fish sauce with chilies on the side.
Remember: The key to great sinigang is getting the right balance of sour and savory flavors, and making sure your meat is tender while keeping your vegetables crisp.