In some fanfics, it could be an entirely new character. This new character could be an old, reclusive wizard who has been observing Harry for a long time. He sees great potential in Harry and decides to come out of hiding to guide him through a unique training that combines different forms of magic that are not taught at Hogwarts.
It could be Dumbledore. He's always been a guiding figure in Harry's life, so in the fanfic, he might continue to mentor Harry through his special training, teaching him ancient and powerful magic.
Often, the main character would be a young witch or wizard who is eager to become an auror. They might be a new student at the training academy.
In some fanfics, Harry might go through combat training with new spells and dueling techniques. This could include advanced defensive magic like creating more complex Patronuses.
Harry would become more disciplined. His natural leadership skills would be enhanced by the military training, making him even more of a force to be reckoned with.
One interesting plot could be the main character facing a series of extremely difficult and dangerous dark magic challenges during the auror training. Maybe they have to deal with a powerful dark wizard who has infiltrated the training grounds to disrupt the training process.
It could be Sirius Black. Sirius was a very powerful wizard and he had a special bond with Harry. He could have come back in some way to train Harry in some unique magical skills, like how to transform into a more powerful animagus form.
Well, perhaps in this fanfic, Harry Potter could be receiving special training in advanced defensive magic from a reclusive and powerful wizard. This training might include learning spells that are not taught at Hogwarts, like some ancient protection charms.
One possible plotline could be Harry and his friends are forced to undergo military training to defend Hogwarts from a new dark threat. They learn combat spells and strategies.
Darth Vader's training would make Harry more self - reliant. In the wizarding world, Harry often has help from his friends. But Vader would force him to rely on his own abilities more. Also, Harry's perception of good and evil might be blurred. Vader's teachings are not as straightforward as the ones in the wizarding world.
'The Changeling' is a notable fanfiction. It focuses on the character development of a new student at Hogwarts, with a plot full of mystery and magic. This fanfiction is great for training in imagining new storylines within the existing framework of the Harry Potter world.
Well, just based on that title alone, it's difficult to determine its quality. There are so many aspects that make a Harry Potter fanfic great. For example, it could explore new relationships between the characters, or create exciting new magical adventures. But we don't know if 'skull is harry potter fanfic' does any of those things. So, it might be good, it might not.