One challenge could be controlling the assassin's violent tendencies. Since the person is being groomed to be an assassin, it's likely they have a natural inclination towards violence, and Harry has to find a way to temper that while also teaching self - defense.
The assassin's loyalty could also be a big challenge. Harry has to ensure that the person he's raising uses their skills for good and not turn on him or the wizarding world. There might be constant temptations for the assassin to use their abilities for personal gain or be swayed by dark forces, and Harry has to find ways to keep their loyalty and moral compass in check.
It could be that the assassin was initially a victim of some dark wizard's experiment. Harry, being the hero he is, feels responsible for the child and decides to raise him. In the process of raising, he unknowingly nurtures the assassin-like qualities in the child because of the unique circumstances and challenges they face together.
In the fanfic, the main challenges for Harry could be related to the limited time he has. He has his own studies and tasks to attend to, like preparing for exams or dealing with the mysteries of the Chamber of Secrets. Yet, he still has to find time to protect Colin. Also, the magical environment itself can pose challenges. There could be spells that are difficult to counteract while protecting Colin, especially if they are new or dark magic.
One challenge could be the basilisk's own will. Even if Harry has the ability to control it, the basilisk is a powerful and ancient creature with its own instincts. It might resist Harry's control from time to time, especially when it comes to situations that go against its natural behavior, like being made to not attack innocent students.
The Dementors are a huge challenge. Their presence alone can drain his happiness and will to escape. He has to find a way to avoid them or protect himself from their effects.
He also has to deal with the secrecy around wand - making. Since it's a highly guarded art in the wizarding world, he might face opposition from the Ministry of Magic or other wizards who think he's meddling in something he shouldn't. Plus, he has to make sure that the wand he crafts is unique to him and suits his style of magic, which is no easy feat.
One challenge could be dealing with the traditionalist teachers and pure - blood families. They might resist any changes Harry tries to make as they are used to the old ways. For example, if Harry wants to introduce muggle - born friendly policies, some of the old - school pure - bloods might oppose it.
One challenge could be the unfamiliarity with the Fairy Tail world. Different rules of magic and different types of magical creatures might be new to Harry. Another is that the Fairy Tail characters themselves might be very powerful and have their own unique abilities that Harry has to figure out how to counter.
Obviously, Harry and Charlus Potter are the main characters. Harry as the one being raised, and Charlus as the one doing the raising.
It could be a new character, like an assassin from a far - off land who comes to Hogwarts under false pretenses. They have their own set of skills and motives that are different from the regular characters in the Harry Potter series.
It could be some Death Eaters who are causing chaos at the World Cup. They might be trying to disrupt the event and target Harry.