Fish eaters and insect eaters are sometimes indicated separately by the terms piscivores and insectivores respectively.
Obligatory carnivores need to eat meat to survive. Eggs and bone marrow can be part of their diet but meat is the most important. The digestive system of these animals is unable to digest vegetable food. In fact, plants are sometimes deliberately eaten to induce a vomiting reflex. For this reason cats sometimes eat grass.
And yet there are vitamins and minerals that are not present in meat, and meat is also no source of fibres. The carnivore receives these by eating the contents of their prey’s intestines. Also the manure of other (herbivore) animals can be a source of these nutrients. So also carnivore animals, which at first sight seem to eat meat only and which also have teeth that are specialized for this, eat plant material.
Besides carnivore animals there also exist carnivore plants (usually insect eaters) en carnivore fungi. These fungi live of amoebas, nematodes and springtails.