The essential thing is that sooner or later you have to come up with the move Re8. You only need the mental flexibility to take a step back after you have failed to find a solution via a series of checks, and look for additional motives.
Personally I saw Re8 immediately, but discarded it because it didn't seem to inconvenience the white queen too much. Then I tried to find a mate with forced checks. When this didn't seem to work, I remembered Re8 and found the solution.
In my experience solving tactical positions often come down to finding the necessary motives and putting them in the right order. If you don't find the right order, maybe you are still missing a motive.