Pickled Jalapeño and Red Onion: In a small saucepan set over medium-high heat, combine the lime juice, vinegar, sugar, salt, and jalapeño. Bring the mixture to a simmer, stirring until the sugar dissolves, about 2-3 minutes.
Add the onion to a bowl or container (that has a lid) and pour the warm vinegar mixture over top. Let cool for 15 minutes then place in the refrigerator and chill for at least 30 minutes.
For the carnitas: Trim any excess fat off of the pork shoulder and cut it into 2" pieces. Place the meat into a large dutch oven with a lid. Add the lime juice, orange juice, garlic, serrano pepper, chili powder, coriander, cumin, and salt. Add water to cover the pork (level to the top of the meat). Bring the mixture to a boil, then cover and reduce to medium-low, cook for 30 minutes. Remove the lid and continue cooking on medium (or a simmer) for 2 hours.
At the very end, the liquid should have reduced substantially. Turn the heat up to medium-high and cook until all of the liquid has been absorbed. Carefully stir the pork until it becomes brown and crispy on the edges, but be careful not to burn it! Remove and serve immediately.
Notes
-Pickled peppers and onions can be made up to 3 days in advance.