Is it permissible to break one's fast to enhance academic achievement when the exam is in two days, given the desire to earn the reward for fasting these days?

The first ten days of Dhu al-Hijjah are the best days in the world. Righteous deeds during them are recommended, and fasting during them is recommended, not obligatory. So fast what you are able to, especially the Day of Arafah. Increase in righteous deeds such as remembrance (dhikr), supplication (du'a), reciting the Quran, prayer (salat), and charity (sadaqah). Do as much good as you can.