If you start a new game of Lego Harry Potter Years 1-4 will you keep the trophies you have earned on the first play through and only need to achieve the ones the won't unlock? Animagus is the only trophy that won't unlock for me.
If you begin a new game, you will retain all previously collected trophies. In your case, Animagus will still be the only locked trophy.
Often, you'll find mutually exclusive trophies i.e. two you can't get in the same play through. An example of this would be Dishonoured's no-kill achievement and the kill-using-all-gadgets achievement.
Additionally, as per Robotnik's comment, you will often only get one opportunity to achieve a trophy, meaning you might need to make multiple playthroughs to try and get them.