While the existing body of research has exhaustively examined several Sustainable Development Goals (SDGs), it fails to adequately reflect the significance of trade-offs and synergies among the SDGs. This study aims to address the existing gap by doing a complete analysis of the SDGs in developing nations, specifically examining the trade-off relationship between SDG-1, pertaining to poverty reduction; SDG-10, concerning reducing inequality; and SDG-13, focusing on environmental activities. The analysis encompasses a sample of 40 developing countries. To accomplish this, a Generalized Method of Movement (GMM)-style Panel-Vector Autoregressive (PVAR) model is utilized, with carbon emissions (CO2Em) serving as a measure for environmental volatility. The findings confirm the existence of the Environmental Phillips Curve (EPC), which signifies a trade-off between SDG-1 (poverty), SDG-10th (inequality), and SDG-13th (CO2Em). Additionally, the processes of industrialization, trade, and population expansion have adverse effects on the attainment of SDG-13. Conversely, industrialization and trade can contribute positively towards SDG-1. A conventional sys-GMM model is utilized for the robustness check, supporting the main findings acquired from the GMM-style PVAR model. Lastly, based on empirical findings, significant policy implications are suggested for the achievement of SGDs.