One challenge could be controlling Kurama's powerful chakra. It's so immense that Naruto might struggle not to be overwhelmed by it. If he can't control it well, he could end up harming himself or losing control during the exam.
Also, Naruto might face the challenge of secrecy. Kurama is a powerful and dangerous force. If word gets out that Kurama is training Naruto directly, it could attract unwanted attention. Enemies might target Naruto to stop him from getting stronger. So Naruto has to keep the training a secret while still trying to show improvement in front of his friends and sensei. This means he has to be careful about when and where he practices the new skills he learns from Kurama.
Another challenge is probably time. The Chunin Exams are approaching fast, and Kurama's training might be intense and time - consuming. Naruto has to balance learning new skills with getting enough rest and also preparing in other aspects like studying about his opponents. He can't afford to burn out or neglect other important parts of his preparation. For example, he still needs to keep up with his regular ninja training with Kakashi and also learn about the rules and layout of the exam area.