As the world grapples with pandemics and increasing stress levels among individuals, heart failure (HF) has emerged as a prominent cause of mortality on a global scale. The most effective approach to improving the chances of individuals' survival is to diagnose this condition at an early stage. Researchers widely utilize supervised feature selection techniques alongside conventional standalone machine learning (ML) algorithms to achieve the goal. However, these approaches may not consistently demonstrate robust performance when applied to data that they have not encountered before, and struggle to discern intricate patterns within the data. Hence, we present a Multi-objective Stacked Enable Hybrid Model (MO-SEHM), that aims to find out the best feature subsets out of numerous different sets, considering multiple objectives. The Stacked Enable Hybrid Model (SEHM) plays the role of classifier and integrates with a multi-objective feature selection method, the Non-dominated Sorting Genetic Algorithm II (NSGA-II). We employed an HF dataset from the Faisalabad Institute of Cardiology (FIOC) and evaluated six ML models, including SEHM with and without NSGA-II for experimental purposes. The Pareto front (PF) demonstrates that our introduced MO-SEHM surpasses the other models, obtaining 94.87% accuracy with the nine relevant features. Finally, we have applied Local Interpretable Model-agnostic Explanations (LIME) with MO-SEHM to explain the reasons for individual outcomes, which makes our model transparent to the patients and stakeholders.