The conflict between socioeconomic development and ecological environmental protection is the main challenge facing sustainable development in underdeveloped mountainous areas. Exploring synergies and trade-offs, maximizing synergies between goals, and minimizing trade-offs among sustainable development goals are effective measures to promote the achievement of the regional 2030 Agenda for Sustainable Development. In this study, an interaction analysis of 14 Sustainable Development Goals (SDGs), 42 targets, and 51 indicators at the municipal scale between 2010 and 2020 was carried out using statistical and network analysis methods in Lincang, Yunnan Province, China, which is an underdeveloped mountainous area. This study showed that the synergies among the SDGs in Lincang were significantly greater than the trade-offs. The indicators with significant synergies were strongly associated with the goals of no poverty (SDG1) and good health and well-being (SDG3), while the indicators with prominent trade-offs were responsible consumption and production (SDG12), climate action (SDG13), and peace, justice, stronge institutions goals (SDG16). Meanwhile, there were significant synergies within and among the three dimensions of essential needs, objectives, and governance; however, there were also trade-off indicators. Under financial constraints, priority should be given to promoting SDG1 and SDG3 (poverty-free and good health and well-being), which have significant synergies, and to enhancing the conservation of terrestrial and aquatic ecosystems so as to exploit the synergies among the indicators and contribute to the achievement of the regional 2030 Agenda for Sustainable Development.