Applying the Strangler Fig Pattern to legacy monoliths: practical challenges?

We're considering using the Strangler Fig pattern to migrate a rather large and old monolithic application to microservices. The monolith handles everything from user management to core business logic and reporting. Has anyone successfully applied this pattern to a truly complex, interdependent legacy system? What were the biggest practical challenges you faced? I'm particularly interested in strategies for data migration and ensuring transactional integrity during the transition, as well as managing the increasing complexity of a hybrid system for an extended period.