The complexities inherent to leukemia, multifaceted cancer affecting white blood cells, pose considerable diagnostic and treatment challenges, primarily due to reliance on laborious morphological analyses and expert judgment that are susceptible to errors. Addressing these challenges, this study presents a refined, comprehensive strategy leveraging advanced deep-learning techniques for the classification of leukemia subtypes. We commence by developing a hierarchical label taxonomy, paving the way for differentiating between various subtypes of leukemia. The research further introduces a novel hierarchical approach inspired by clinical procedures capable of accurately classifying diverse types of leukemia alongside reactive and healthy cells. An integral part of this study involves a meticulous examination of the performance of Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) as classifiers. The proposed method exhibits an impressive success rate, achieving approximately 90\% accuracy across all leukemia subtypes, as substantiated by our experimental results. A visual representation of the experimental findings is provided to enhance the model's explainability and aid in understanding the classification process.