There are multiple weapons that you can use against the alien, but they only slow down or distract the alien, it cannot be killed. Since there is only one alien in the game it makes sense that you cannot kill him. The weapons you have access to are quite powerful, but they are meant to be used in a way to distract or ‘frighten’ away the alien so he doesn’t kill you.
There are other human and synthetic enemies in the game that can be killed, but the alien cannot. The developers have stated that it is possible to complete the game without killing a single enemy in the entire game.