Oxygen breathing is not required to support the life; most of organisms can also use other metabolic pathways to get the energy. Removing all oxygen from the Earth atmosphere would be apocalyptic of course, with most of animals dying immediately, however some plant species may survive on anaerobic breathing during the night (plants produce plenty of their own oxygen as long as photosynthesis is running). Anaerobic bacteria already living in oxygen-less places of Earth would not notice anything wrong happening and will take over leading the evolution.
Disappearance of the ozone layer will increase the UV radiation. However this work shows that sea water (with usual particles in it) also provides efficient protection, so water organisms should probably survive, even if affected. UV-proof shells and scales may evolve.
However oxygen is also an important part of protein, DNA and cell membranes that are all very essential components of every living cell, as well as water that is also essential. Nitrogen and fluorine are not replacements, these elements have very different properties, same about hydrogen. Sulfur is somewhat similar and may substitute oxygen in some degree, but all molecular composition of life must be redesigned.