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.
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.
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.
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.
Well, without having read it, it could be a fanfic that focuses on Harry Potter's inner strength. The 'through the fire' part might symbolize the difficulties he has to endure. It could involve his battles against dark forces, not just Voldemort, but also other threats in the wizarding community. And it might explore how he overcomes these obstacles with the help of his friends.
'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.
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.