This page contains a detailed description of Zoologist trophy in Shadow of the Tomb Raider. This achievement is awarded for the collection of a total of 20 animals.
You won't unlock this trophy during your standard bow hunting. You must first unlock the Owl's Meal skill. Fortunately, it only requires 1 development point.
From the moment you unlock this skill, you can find beetles and spiders in the game world. The survival instinct (picture above) is very helpful in locating them, but you can also manage without it. The game accepts catching each of these creatures (in order to get poison or venom) and you have to find 20 of them in total.
You can get this trophy in the Peruvian jungle, but in all other major game locations you can find spiders and beetles too.