The Trilobite ship seems to only have visual range, so if you're hiding against a building or in an alley then it won't shoot at you.

You can take them down if you need to but, once you learn that it's a game of hide and seek then it just adds an extra layer of positioning to the fights. On higher difficulty there will be quite a few of them and they take a lot of secondary resources to deal with, better to dodge them and use your secondary for fighting the ground squids.