breathe has 8 distinct synonyms spread across 3 of its 9 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
be alive
“Every creature that breathes”
impart as if by breathing
“He breathed new life into the old house”
allow the passage of air through
“Our new synthetic fabric breathes and is perfect for summer wear”
manifest or evince
“She breathes the Christian spirit”
take a short break from one's activities in order to relax
reach full flavor by absorbing air and being let to stand after having been uncorked
“This rare Bordeaux must be allowed to breathe for at least 2 hours”
Synonyms, antonyms and the broader and narrower relations for breathe come from Princeton University’s WordNet. Full sources and licences.