Heat oven to 300 degrees. Score meat’s skin with a sharp knife, making a cross-hatch pattern. Pulse garlic, onion, oregano, cumin, chili, salt and pepper together in a food processor, adding oil in a drizzle and scraping down sides as necessary, until mixture is pasty. (Alternatively, mash ingredients in a mortar and pestle.) Blend in the vinegar.
Rub this mixture well into pork, getting it into every nook and cranny. Put pork in a roasting pan and film bottom with water. Roast pork for several hours (a 4-pound shoulder may be done in 3 hours), turning every hour or so and adding more water as necessary, until meat is very tender. Finish roasting with the skin side up until crisp, raising heat at end of cooking if necessary.
Let meat rest for 10 to 15 minutes before cutting it up; meat should be so tender that cutting it into uniform slices is almost impossible; rather, whack it up into chunks. Serve with lime.