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Before Montague courted Romeo's mom, he had already courted another woman. A Capulet actually. Soon after she was pregnate, Montague dumped her to marry Romeo's mother. The woman left the castle to live in the town and had baby Tybalt. Not to long after she had Tybalt she died. He hated Montague from that day onward. So Tybalt is helping Juliet with her revolution against Montague because he blames his mother's death on him.
In the anime he tells of the planned assassination of Benvoilo's family who are allies of the Montagues as well as the Capulets. He and his family is hidden by Conrad who doesn't want to hide them at first since they're always seen around the Montagues. Tybalt later on aids Benvolio's family for a short while when the assassination is supposed to take place.
It is later revealed by Tybalt that he has hidden spies all over Neo Verona dressed like he is getting information on the Montagues so Juliet and her allies have an easier time taking them down.
Conrad also admits he may know the truth about Tybalt but so far hasn't said anything since he is still unsure if he is right or not.