Stir the brown sugar, salt, paprika, garlic powder, oregano, basil, chili powder, cumin, and coriander together in a small bowl.
Trim any large pieces of fat from the pork and cut it into 1-inch cubes. Sprinkle the spice mix over the pork and rub it in until every piece is coated.
With the Instant Pot still off, arrange the pork in the inner pot and let it rest for 5 minutes.
Halve the lime lengthwise, squeeze the juice over the pork, and drop both halves into the pot. Pour in the ½ cup water.
Lock the lid, turn the valve to Sealing, and cook on Manual (Pressure Cook) at high pressure for 40 minutes.
When the cook time ends, allow the pressure to come down naturally for 15 minutes, then carefully release whatever pressure remains.
Turn the oven broiler to high (500°F if your oven has a setting) and line a baking sheet with foil.
Lift the pork onto the baking sheet with a slotted spoon, leaving the limes behind. Pull it apart with two forks and spread it out.
Broil for about 5 minutes, until the edges are browned and crisp. Check often so it doesn't burn.