Soft skills are the key characteristics for students’ success and wellbeing in the 21st century, but they were only rarely studied contemporarily or integrated into comprehensive models of self-regulated learning. This makes it difficult to understand the role that specific skills have above and beyond the others and how they work together to favor students’ achievement and life satisfaction. For this reason, in a sample of 585 students (10–18 years old), we applied an exploratory network analysis and studied three crucial soft skills (i.e., adaptability, curiosity, and perseverance) and their contemporary network of inter-relationships with a host of functional study-related factors, including self-regulated learning strategies, motivation, emotions, cognitive abilities, academic achievement, and life and school satisfaction. Results show that the three soft skills play a positive role within the school context through their association with the majority of the study-related factors that mediate their relationships with academic achievement. Importantly, the results differentiated adaptability (which mainly relates with wellbeing and emotional variables), perseverance (which relates with the cognitive and behavioral aspect of learning), and curiosity (which bridges the connection between the other skills and relates with emotional and behavioral variables) in the school context. Overall, these findings contribute to the deepening of the theoretical framework on soft skills and their role as part of a successful learning profile, and inform us about the possible effectiveness of intervention on soft skills for students’ achievement and wellbeing.