This area of law is very complicated. This is why the attorney needs to criminal records to verify what can be done. If the amount of credit card fraud is in excess of $10,000.00, it is probably considered an aggravated felony.
There are many things that are important and even the smallest detail could make the biggest difference. For example, all the following are important: when the crime was committed and when the conviction was entered, if it is actually a conviction, how the conviction was entered (jury trial or plea bargain), if the crime is classifiable as an aggravated felony, if the crime can be classified as a crime involving moral turpitude, how the crime is treated by state law and how it is treated by federal law, if it was a plea agreement, if immigration warnings were given before acceptance of the plea, how those warnings were given if they were given, if the person was a Lawful Permanent Resident (LPR) at the time of commission of the crime, and how long they had been an LPR before the crime was committed.
So you can see how complicated this can be. There are waivers (forgiveness) available and there is other relief from deportation such as Asylum, Withholding of Removal, Convention Against Torture, and Cancellation of Removal.
In order to really explore all these possibilities, you should look for an experienced immigration attorney and take all the documentation you can about the criminal charge/conviction. If you aren't satisfied with your current attorney, you can look for an experienced attorney by going to www.ailalawyer.com.