(someone) puff (their) chest out

Translations
задирать нос; важничать
He likes to puff his chest out when he talks about his achievements.
Он любит задирать нос, рассказывая о своих достижениях.
Definitions
To puff one's chest out means to physically push one's chest forward, often as a display of pride, confidence, or bravado. Figuratively, it refers to acting in a proud, self-important, or boastful manner.
Words
someone

pronoun
кто-то
puff

verb
выпячивать
their

article or possessive pronoun
свою
chest

noun
грудь
out

adverb
наружу