We know at least something approaching the full truth about Amaral's lies and we know they are lies by comparing what he has written (or said) with what is written in the files.
Making "claims" of defamation against Amaral, not so much claims as facts.
If you read the first judgement carefully you will find that the judge didn't see anything wrong with the book. On page 34 she says there's nothing new in the book. What it says was said by the investigation, it led to the McCanns being made arguidos and it has been said by others.
In order to penalise Amaral her judgement brings in his obligations as a retired policeman. Using some rather complicated mental gymnastics she decides that he has breached judicial secrecy and failed to allow the McCanns the presumption of innocence. Both of these requirements are imposed on a retired policeman, she argues, and they restrict his freedom of speech.
All the Appeal judges had to do then was show that being a retired policeman did not impose those obligations on Amaral, he enjoyed full unrestricted freedom of speech, and her judgement was shown to be wrong.