General:
* Big mouth: This refers to someone who talks too much, often bragging about themselves.
* Blow one's own horn: This means to brag about one's achievements.
* Full of oneself: This describes someone who is arrogant and thinks highly of themselves.
* Stuck-up: This describes someone who is arrogant and condescending.
* Toot one's own horn: This is another way of saying "blow one's own horn."
More specific:
* A peacock: This is a metaphor for someone who is excessively vain and showy.
* A braggart: This refers to someone who boasts about themselves excessively.
* A show-off: This describes someone who tries to impress others with their abilities or possessions.
The best idiom to use will depend on the specific context and the tone you want to convey.