Rinse halibut and place on a plate. Pour 4 tablespoons lime juice over fish; sprinkle with 1 teaspoon salt and the pepper. Cover and chill for 20 minutes.
Meanwhile, pour 1/2 inch oil into a 10- to 12-inch nonstick frying pan with sides at least 2 inches tall over medium-high heat. When surface looks rippled, gently lower a tortilla into oil and cook, turning once, until crisp, 1 to 2 minutes total. Transfer to paper towels to drain briefly. Repeat to fry remaining tortillas. Discard oil and wipe pan clean.
In a small bowl, stir together yogurt, sugar, chili powder, and the remaining 1 tablespoon lime juice and 1/2 teaspoon salt.
Set pan over medium-high heat. When hot, add fish to pan along with lime juice, cover, and cook until opaque in the center (cut to test), 10 to 12 minutes. Break fish into flakes with a fork.
Pit, peel, and slice avocado. Place a fried tortilla on each plate and layer equally with shredded cabbage, flaked halibut with its juices, yogurt sauce, avocado slices, cilantro leaves, and fresh salsa.