There are three ways to approach character analysis to gain information for writing a character sketch. The first is to examine the character's own words and actions. The second is to examine what other characters say about him and do as a result of his words and actions. The third is to compare one character to another. There is some very good evidence available from examining Tybalt this way.
Starting at Tybalt's first entrance, Benvolio (a Montague) is trying to stop the servants from the two houses of Capulet and Montague from battling each other in the streets of Verona. He has drawn his sword and "[b]eats down their swords." This is significant as a point of comparison against Tybalt.
Tybalt now enters the scene. He rejects Benvolio's explanation and invitation to help stop the servants' fighting and cries, "Have at thee, coward!" as he lunges with his sword at Benvolio. In comparison, while Benvolio cries for peace,
BENVOLIO: I do but keep the peace: put up thy sword,
Or manage it to part these men with me.
Tybalt cries for hatred and blood shed,
TYBALT: As I hate hell, all Montagues, and thee:
Have at thee, coward!
Tybalt's words and actions reveal him to be a violent, angry, ill-reasoning young man who thinks not of facts and consequences but only of feelings and passions. He speaks of hatred and he pursues violence. As his later encounter with Mercutio shows, he pursues these to the death.
In a later Act III comparison, Tybalt meets his match for anger and violence in Mercutio. Yet, Tybalt goes even further and proves the truth of his words of hatred and anger by stabbing Mercutio under Romeo's arm while the latter is trying to stop the fight. After thus ignoring Romeo's pleas for love and peace, Tybalt stabs Mercutio to his death "and flies with his followers."
What Tybalt reveals by his actions is confirmed by what he reveals in his words. When he hears Romeo's voice at his father's ball, he calls for his sword and intends instant murder:
TYBALT: Fetch me my rapier, boy. What dares the slave
Come hither, ...
To strike him dead, I hold it not a sin.
Further confirmation comes in the form of Lord Capulet's words to him and Benvolio's report of him. First, at the ball, when Capulet hears Tybalt's outrage against Romeo, Capulet gives his criticism of Tybalt's preposterous behavior that threatens to "make a mutiny among [Capulet's] guests!"
TYBALT: I'll not endure him.
CAPULET: He shall be endured:
What, goodman boy! I say, he shall: ...
Am I the master here, or you?
Be quiet, or ... For shame!
I'll make you quiet.
When questioned in Act I by Lord Montague, Benvolio says of Tybalt that he drew and swung his sword about his head, cutting the wind, in an imperious manner and, rather than aid in parting the fighting, joined in and worsened it:
BENVOLIO: I drew to part them: in the instant came
The fiery Tybalt, with his sword prepared,
Which, as he breathed defiance to my ears,
He swung about his head and cut the winds,
From Tybalt's own words and actions in Acts I, II and III; from the comparisons to Benvolio in Act I and Mercutio (and Romeo) in Act III; from Benvolio's and Capulet's remarks in Acts I and II, you can analyze Tybalt's character to gather information about him from which to write a character sketch of Tybalt.