When is a character out of order? If it comes alphabetically before the previous character, right? So compare each character (except the first) to the previous character, and if it's smaller it's out of order.
When is a character a duplicate? If it already was encountered in the String, right? Now, you can't simply compare a character to its previous character to see if it matches, because a String of "tat" still has duplicates. So you need to a) compare each character with all characters before or after it (both is not necessary), or b) keep track of which characters you already encountered and see if the current character is one of those.