The key quote on why Duterte is popular outside the elite circles:
Since the fall of dictator Ferdinand Marcos in 1986, the Philippines has been mostly ruled at local and national levels by a small group of families backed by powerful businessmen -- a system that has helped entrench one of Asia's biggest rich-poor divides. The current president, Benigno Aquino, belongs to such a clan and has in the final stages of his rule been fiercely criticised for what many voters regard as perpetuating an economic model that favours the wealthy.
and here is an older article about the way he did it.
however, when it takes forever to get justice, one can be less than sympathetic to those who prey on the poor and middle class.
and the InC is backing him now, which will give him cover: probably gifted something to do it, but they also are connected with left wing socialist types here.
he also has friendly links to the NPA, the local communist "militants", leading some to worry that the army will simply hold a coup to overthrow him if elected.
Saint Miriam, who would be a good president except for being sick, too honest to steal money and buy votes, and being in the bottom of the polls, summarizes it this way:
So we have an NPA candidate. Will the CIA, which has a link to the husband of Grace Poe, allow the communists to win? So first of all there is a conflict between the NPA and the CIA,” she went on.