Drain the fish and pat the pieces dry with a paper towel. Have a plate lined with paper towels or a cut-open brown paper bag at the ready.
In a large, heavy-bottomed pot, heat at least 2 to 3 inches of oil over medium heat until it reaches 360°F (182°C) on a deep-fry or candy or instant-read thermometer.
Remove the tempura batter from the refrigerator and stir to recombine.
Dredge a few pieces of fish at a time in the batter, turning to coat them evenly. Gently lower a couple pieces of fish into the oil, adding a couple more pieces every 30 seconds. Fry no more than 4 pieces at a time. Fry the fish, turning as needed, until the pieces are crisp, light golden brown, and floating on the surface of the oil, about 2 1/2 minutes. Monitor the temperature of the oil throughout frying, letting the oil return to proper temperature between batches; to ensure crispness, it must remain a constant 360°F to 380°F (182°C to 193°C).
Using a fine-mesh skimmer, transfer the fried fish to the paper towel-lined plate or brown paper bag to drain. Repeat with the remaining fish and batter, being sure to remove any flecks of floating fried batter in between batches.