Preheat your oven to 400°F and place the corn tortillas directly on the oven rack for 8 to 10 minutes until they are crisp and golden.
In a medium bowl, toss the peeled and deveined shrimp with the chili powder, sea salt, black pepper, and half of the juice from the lime.
Heat the olive oil in a large skillet over medium-high heat until shimmering.
Add the shrimp to the skillet in a single layer and sauté for 2 to 3 minutes per side until they are pink, opaque, and slightly charred.
While the shrimp cooks, mash the avocado in a small bowl with a pinch of salt or slice it thinly to prepare for assembly.
Spread the avocado onto the crispy tostada shells, then layer on the shredded cabbage and thinly sliced radishes.
Top the tostadas with the sautéed shrimp, garnish with fresh cilantro, and drizzle the remaining lime juice over the top before serving.