The students' progression and attainment gap are considered as key performance indicators of many universities worldwide. Therefore, universities invest significantly in resources to reduce the attainment gap between good and poor performing students. In this regard, various mathematical models have been utilised to predict students' performances in the hope of informing the support team to intervene at an early stage of the at risk student's at the university. In this work, we used a combination of institutional, academic, demographic, psychological and economic factors to predict students' performances using a multi-layered neural network (NN) to classify students' degrees into either a good or basic degree class. To our knowledge, the usage of such an extended profile is novel. A feed-forward network with 100 nodes in the hidden layer trained using Levenberg-Marquardt learning algorithm was able to achieve the best performance with an average classification accuracy of 83.7%, sensitivity of 77.37%, specificity of 85.16%, Positive Predictive Value of 94.04%, and Negative Predictive Value of 50.93%. The NN model was also compared against other classifiers specifically k-Nearest Neighbour, Decision Tree and Support Vector Machine on the same dataset using the same features. The results indicate that the NN outperforms all other classifiers in terms of overall classification accuracy and shows promise for the method to be used in Student Success ventures in the universities in an automatic manner.