Preheat your oven to 300F. For slow cooker method, see notes below.
Cut the pork shoulder into 4 smaller pieces. If there's any string around the roast, remove it. Don't cut any of the fat off.
In a small bowl, stir together the chili powder, oregano, cumin, salt, and pepper. Coat the pork pieces in the spice mixture, and add them to a Dutch oven.
Add the onions, jalapeno peppers, garlic, chicken broth, orange juice, and lime juice on/around the pork.
Cover and cook for 2 hours, then uncover and cook for another 1.5 hours or until it's fall-apart tender.
Take the meat out of the Dutch oven and place it on a baking sheet. Shred it with two forks. Ladle about a cup of the leftover cooking liquid over top and toss to coat. You can either serve it as-is or proceed to the next step to crisp up the meat (recommended!), using one of two methods.
Method 1 (Oven): Move the rack to the top third of the oven and set your oven to broil. Transfer the baking sheet to the oven and broil until you've got some nice crispy bits. I typically check after 5 minutes and then pop it back in for more time as needed.Method 2 (Skillet): Add the meat and some cooking juices to a skillet and cook over medium-high heat until one side is crispy. The juices should have enough fat, but if needed, add some oil or lard (I reserve bacon grease when I cook it and keep it in a jar in the fridge). Do the skillet method in batches. Serve in tacos or as desired.
For leftovers, I don't discard the remaining cooking juices. I just mix them in with the rest of the shredded pork as it helps to keep it moist. The juices will congeal when cooled (creating lard), which is great for when you want to reheat leftovers. See blog post above for more leftovers/storage/reheating tips.