Combine the olive oil, garlic, chipotle pepper, lime juice, cumin, paprika, salt, and pepper in a bowl. Add the shrimp and toss everything together until each piece is fully coated. Let the shrimp sit in the refrigerator for about 20 minutes so the flavors have time to soak in.
Thread the shrimp onto skewers so they're easy to flip without losing any to the grates. Grill over medium-high heat for around 2 to 3 minutes per side, until the shrimp turn opaque and pick up a light char. Pull them off right away so they don't overcook and turn rubbery.
While the shrimp marinate, whisk together the yogurt, chipotle adobo sauce, lime juice, cilantro, and a pinch of salt in a small bowl. Taste it and adjust the heat by adding more or less adobo sauce. Cover and refrigerate until you're ready to assemble the tostadas.
Mash the avocados with a fork, leaving a bit of texture instead of making it completely smooth. Stir in the diced red onion, lime juice, salt, and pepper. This layer is what holds everything else in place, so make sure it's spread evenly.
Spread a generous layer of the mashed avocado over each tostada shell. Add a small handful of shredded cabbage, then top with a few pieces of grilled shrimp. Finish with a drizzle of chipotle crema, a sprinkle of queso fresco, and a few cilantro leaves.