Here are techniques you will often combine:
SCC + DP: Compress graph to DAG, then run DP on the DAG MST + Bridges: Find MST, then find critical edges within it DSU + MST: Kruskal's algorithm uses DSU to avoid cycles -SAT + SCC: Build implication graph, find SCCs to check satisfiability
When you see a hard problem, try to break it into two simpler problems that each use one technique. This decomposition skill is what separates strong problem solvers.