In a food processor, pulse together cilantro, garlic, oregano, cumin, salt, pepper, vinegar and lime juice.
Using a pointy knife, poke holes into the pork shoulder. Rub the seasoning mixture all over the meat pushing some of the seasoning into the small holes. Cover and place in the refrigerator. Let marinate overnight.
The next day, place the pork shoulder on the slow cooker and cover with water. Add enough water to cover at least 3/4 of the meat inside the slow cooker. Cook on low for about 8 hours.
Once the meat is tender, carefully transfer it to a roasting pan. Roast in the oven at 450 degrees until brown and crispy, about 1 hour. Take out of the oven and let rest for 15 minutes. Shred the meat using two forks.
Serve with a side of tostones, rice or tortillas.