I have to address my love for this graphic novel. It's a really well paced, and entertaining. There are criticisms, some justified, some not (MAYBE SPOILERS?);
1)Failure to save the little girl despite having the 'gadgets' can be explained as this is only the fourth 'Legend of the Dark Knight' story, so the lack of tools is because we are shown a young batman.
2)Batman written out of character can be explained by the personality affecting drugs which are VERY STRONG and he has been taking for at least THREE MONTHS.
3)The fact he is so distraught over the girls death is self-explanatory, as well as the fact that early batman would find it difficult to come to terms with letting a drowning girl die, let alone any other man.
4)Perhaps he should have picked up on the Father's unsympathetic response, however Batman is so distraught on what he let happen that he may have been a little distracted to notice details such as that
5)Alfred coming with him on the island is the only thing that didn't make sense to me, but may be due to the fact that he needed someone to fly him there, and Batman is not yet a confident flyer...
For all the questionable points, there are more amazing moments to counteract. The writing for Alfred is nailed in this than most others. He is a witty character who maintains Batman's life, exchanges conversation to help boost his thought process, and tries to be a moral compass, suggesting to read when Batman is physically obsessed and shows his displeasure when Batman crosses the line peacefully. Tears welled up in scene where he is standing outside the Batcave, helping Batman with the addiction - Worth it for this scene ALONE!