Heat a heavy skillet on medium to medium-high, for about 2-3 minutes, add the oil. Immediately add the fish and cook it until the bottom is firm and crispy-brown. While it's cooking, lightly salt and pepper the uncooked top.
Turn the fish over, cook until browned on second side, and season with salt and pepper the cooked upper side.
Remove fish from pan and cut up roughly with two forks. Squeeze lime juice liberally over fish.
Holding two hot, stacked tortillas in one hand, add fish, kimchi, sliced onion, and cilantro leaves to the taco. Serve immediately.