It may be your employer, rather than you, who was the attorney's client. It's not always possible for a third party (you, in this case) to sue for malpractice if you weren't the actual client.

Nevertheless, if the law firm developed an attorney-client relationship with you, then they would owe you a fiduciary duty and could be liable for an error on your PERM application. It does not matter who paid the law firm. The specific facts of your case, such as communications with the attorney, would be indicative if this relationship was created.

Even if no attorney-client relationship was formed Colorado recognizes the legal concept of third party beneficiary to a contact. A third-party beneficiary may enforce a contract only if the parties to that contract intended to confer a benefit on the third party when contracting. Here you would be the beneficiary and it sounds reasonable that they intended to benefit you.