Trim any excess surface fat from the pork shoulder and cut into large chunks.
In a small bowl, whisk together the smoked paprika, garlic powder, onion powder, sea salt, and black pepper.
Rub the spice blend evenly over all sides of the pork pieces.
Place the seasoned pork into a slow cooker and pour the apple cider vinegar over the top.
Cover and cook on low for 7-8 hours or on high for 4 hours until the meat is tender enough to fall apart.
While the pork cooks, shred the green cabbage and finely chop the fresh cilantro.
In a medium bowl, whisk the Greek yogurt and lime juice together, then toss with the cabbage and cilantro to create the slaw.
Once the pork is finished, remove it from the slow cooker and shred with two forks, discarding any remaining large pieces of fat.
Briefly warm the corn tortillas in a dry skillet over medium heat until pliable.
Fill each tortilla with a generous portion of pulled pork and top with the creamy lime slaw.