Shakespeare portrays Tybalt as extremely hot-tempered. Of all the characters, he is one that prefers instigating fights over creating peace.
One instance we see of Tybalt's hot temper is in the opening scene. After the Capulet servants begin the fight with the Montague servants, Benvolio tries to separate them, saying, "Part fools! / Put up your swords. You know not what you do." However, Tybalt enters the scene and seeing Benvolio's sword drawn, which he was using to stop the fighting, challenges Benvolio, saying to him:
What, art thou drawn among these heartless hinds?
Turn thee, Benvolio! look upon thy death. (Act 1, Scene 1)
We further see evidence of Tybalt's violent temper when he says, "I hate the word [peace] / As I hate hell, all Montagues, and thee."
Another instance we see of Tybalt's hot temper takes place at Capulet's ball. When Tybalt spies Romeo at the ball, his immediate assumption is that Romeo has come "to fleer and scorn" their party, meaning to make fun of their party. Tybalt feels insulted and promises to kill Romeo. When Capulet stops him, arguing that Romeo is reputed in Verona to be "a virtuous and well-govern'd youth," Tybalt feels even more insulted, vowing revenge on Romeo.
Tybalt is an arrogant man who belongs to the Capulet family. He absoltely hates the Montague family, and challenges Romeo many times to a duel. He kills Mercutio, and as revenge Romeo kills Tybalt. I hope that helps! :)