How to Make It
Arrange sea bass pieces in a large glass or ceramic bowl; sprinkle all over with salt. Gently toss until fish is evenly coated. Add ice, and fold gently with a rubber spatula until salt dissolves and ice starts to melt and pool on bottom of bowl, about 5 minutes. Cover with plastic wrap, and refrigerate until fish is firm, about 1 hour, folding gently every 15 to 20 minutes.
Whisk together lime juice, Worcestershire sauce, soy sauce, sugar, tomato paste, hot sauce, black pepper, and pequin chile in a bowl until tomato paste dissolves and ingredients are fully combined. Set dressing aside.
Thinly slice 1 cucumber to equal 1 cup, and set aside. Dice remaining cucumber to equal 1 cup, and set aside. Cut avocado in half; reserve one half for another use. Cut remaining half lengthwise into 1/4-inch-thick slices, then cut crosswise into 1/4-inch-thick slices to equal about 1 cup. Set avocado aside.
Transfer fish to a colander; discard ice. Rinse fish under cold running water. Arrange fish in a single layer on a cutting board lined with paper towels to absorb excess water; pat fish dry.
Reserve 2 tablespoons dressing. Transfer fish to a clean glass or ceramic bowl. Add red onion, diced cucumber, and remaining dressing. Stir gently to combine. Season to taste with salt and black pepper.
To serve, scoop about 1/4 cup fish mixture onto each tostada. Top evenly with sliced cucumber, avocado pieces, and a drizzle of the reserved dressing. Serve tostadas immediately.