In a medium bowl, combine lime juice, garlic, cumin, chili powder, salt, and pepper. Add fish and toss to coat. Cover and marinate for at least 15 minutes.
Heat a grill or grill pan to medium-high heat. Grill fish for 4-5 minutes per side, or until cooked through.
Meanwhile, prepare the aioli. In a food processor, combine avocado, cilantro, yogurt, mayonnaise, and salt and pepper. Process until smooth.
Warm tortillas in a dry skillet over medium-high heat.
To assemble tacos, place a piece of fish in each tortilla. Top with a dollop of aioli and a sprinkle of cheese. Serve immediately.