Deep sea dwelling creatures do not breathe air. As their bodies do not contain large volumes of air, but contain water instead, the pressure inside them will vary with the pressure of the water outside, and whereas a human's lungs will eventually collapse at depth, an seabed dwelling creature's body will be in equilibrium with its environment. That's why Siguorney Weaver has to breathe that green liquid in The Abyss (which, incidently was one of the very first 12 certificate movies in the UK!).