Cardiovascular diseases (CVDs) are still the primary cause of death globally, and heart disease is the most critical contributor. Precise diagnosis early on prevents poor outcomes, but available diagnosis techniques are typically costly, invasive, and dependent on expert interpretation. This study explores whether artificial intelligence (AI), in the guise of deep learning and bio-inspired optimization, can provide a robust, non-invasive predictive diagnosis of heart disease. Two baseline algorithms, Multi-Layer Perceptron (MLP) and Artificial Neural Network (ANN), were trained and tested on the Cleveland heart disease database. While baseline performance was found to have outstanding predictive capability, this was constrained by sensitivity to hyperparameters. To alleviate this, tuning was performed using the new bio-inspired metaheuristic, the Aquila Optimizer (AO), which draws inspiration from the hunting strategy of Aquila eagles. Experimental results show that AO significantly enhances model performance: the AO-tuned MLP achieved accuracy of 98.05% and ideal precision of 100%, while the AO-tuned ANN produced optimal performance with 98.54% accuracy, 100% precision, 97.09% recall, and a Matthews Correlation Coefficient (MCC) of 0.9712. Convergence of the fitness function confirmed AO's capability to achieve stable and near-optimum solutions in few iterations. Results emphasize the benefit of ANNs for structured clinical data and validate that AO is a phenomenal tool for optimizing neural networks in medicine.