Tybalt is tenacious.

"What, drawn and talk of peace? I hate the word

As I hate hell, all Montagues, and thee."

Tybalt, Romeo and Juliet, Act I, Scene i, Line 61 and 62

Tybalt's tenacity is shown by his refusal to stop feuding with the house of Montague. Instead he perpetuates the feud by challenging Romeo to a duel and killing Mercutio. He first notices Romeo at the Capulet's party. He spends all of the party stewing over how his uncle won't let him fight Romeo. He only hates the Montague family his father and his father's father and et cetera also hated them. He hunts Romeo down because feels his family's honor has been insulted. When Romeo refuses to fight, he is only too happy to duel with Mercutio, simply because he appears to be acquainted with a Montague. Not a Montague himself, merely acquainted with one. His refusal to change his ways and stop feuding ends in many deaths. First Mercutio's death, then his own, and finally Romeo and Juliet's death. Tybalt is tenacious because he is stuck in the past and is resistant to change.