There's actually more than 4 types of fish that you should avoid eating and the types of fish you should not eat due to the high mercury count in these types of fish which can lead to hypertension and even heart problems and heart attacks when you intake too much mercury.
The fish that you should avoid eating and never eat really are.
Tilapia.
Atlantic Cod.
Atlantic Flatfish (Atlantic halibut, flounder and sole)
Caviar.
Chilean Seabass.
Eel.
Farmed Salmon (Atlantic or Wild-Caught)
Imported Basa/Swai/Tra/Striped Catfish (Often Labeled “Catfish”)
Also any type of fish should be only eaten in moderation since it's possible to get mercury poisoning from eating too many fish.
So while fish is a good health food it can actually harm you if eaten too much due to the mercury contained in fish.