We have absolutely no confirmation they need to breathe, we even have more clues they don't in the various movies, and some of the "extended universe" on various media doesn't hesitate to establish they don't.The films establish they breathe.
I've only seen them blowing air to extinct candles or to threaten through a window. This is not the same thing, just like they can have mouths but we're not sure the adult form needs to eat.
[In Alien 1/2/3 (and probably even 4), we never see an adult Alien eat. Some people theorize that in accordance to their biomechanical design, they deal with energy more like a car battery, which would work nicely with the Alien blood.
Also if they eat, why are the hosts' corpses always
left to rot in the coccoons?]
Edit: Of course if I've missed a line, a picture or a scene, by all means tell me. But I would find it bad to assume Aliens eat or breathe, we're already talking about an organism which can reach its adult form in a matter of hours, which has acid for blood, and whose egg form can survive in extreme conditions.