It sounds like you are supposed to demonstrate your understanding of Romeo's perspective of the fight/death scene, how things escalated and what events led to him killing her cousin. Think about how Romeo would speak to Juliet. The tone of the letter would certainly be sympathetic to her loss, but also guilt-ridden and apologetic. He would certainly explain that he tried to stop the situation, but that Tybalt refused to stand down. Go back to that scene and quote what Romeo said to Tybalt (like when he says that he "loved" Tybalt) in order to show that Romeo did his best to calm Tybalt down. Then have Romeo focus on how Tybalt used an intervening opportunity of peace to stab Mercutio. That should be a very persuasive part that could justify Romeo's rage that followed.
Remember to follow the assignment by making sure you have the right amount of paragraphs needed. If it is a 5-paragraph essay, you could write an Introduction, one body paragraph about Tybalt, one paragraph about Mercutio, and one paragraph about Romeo's actions. The conclusion then would be asking forgiveness from Juliet.