There are three punishes to look out for (apart from the Mikiri): the leaping attack (similar to first encounter, but it's not part of a combo here), his long wind-up overhead, and his gunpowder combo. For his overhead you have to make sure not to dodge too early or he'll modify it into a spinning slash. You can also stand slightly to his front-left/right (think of a conal shape) and have it go right past you. Whichever is easier for you. (Note: He normally has hyperarmor during this, but during the second phase I accidentally cancelled it a few times with one hit.) For his gunpowder combo, wait for him to do the shoulder tackle and then quickly run to the right/left and circle behind him once he throws out the explosives.