Big volume/pressure really helps on a radiator. I have a 175 psi at 16cfm compressor and that is not too big. The construction of the radiator can make a difference as to how easily it cleans. A narrow/deep radiator is much harder to clean than a wide/shallow one. Sometimes a pressure washer can be used but dont get carried away or you might get to find out how much fun fin straightening is! Just dont quit once you start with water, once the dirt become wet it will set up even harder once it dries if you dont get it out. Sometimes I leave the engine running to help clear out the debris, although this is probably against every safety rule.
Big air and a small hole for it to come out of, and stay with it till you are done works the best.