Pretty good, but could be even better. Your sentence, “I think if she had decided to write the letter to get credit, she should have written in a careful way” is an example of the 3rd conditional. If you’d like to improve it, it might be better to write it as a mixed conditional. Also, while your word choice is OK (correct and understandable), I’m going to suggest some changes. Here is your grammar, but more succinct, and with better vocabulary, more idiomatic phrasing.:
“I think if she wrote the letter for credit, she should have written it more carefully.”
Explanation of conditionals:
“If she wrote the letter for credit”: This is a past *real* conditional — you believe that she actually did write the letter for credit. That being the case….
“she should have written it more carefully”: This is the 3rd conditional, i.e. contrary-to-fact past. You present this alternate reality as a way of criticizing her (past) behavior.