Due to the fact that this will take place in Central Park with no preparations, this will immediately knock out Pastmaster's Resurrection, unless there are some dead bodies lying around somewhere in Central Park. And while he could potentially animate some of the statues around him or even summon a creature from the past using his Tome of Time, I don't see them holding up too long against The Fool, seeing as he could grind the statues to dust using the sand and strike at the creatures when they least expect it, just as he did with Petshop in the sewers, but probably even easier. The real challenge, I think, is Pastmaster himself. The energy blast from his watch was powerful enough to blow a hole into a bridge that was big enough for cars and trucks to fall through, and he is also a very intelligent individual. However, the biggest problem for Pastmaster is that Iggy is a natural tactician, able to make up strategies on the fly, whereas Pastmaster is more of a schemer and prefers to plan things out ahead of time. Plus, The Fool is a very powerful Stand, able to easily keep up with Silver Chariot, and combining it with Iggy's intelligent planning, could easily pounce on Pastmaster and deal the finishing blow, since the power of The Fool is much higher than Pastmaster's durability. If I missed certain facts coming up with this, please let me know. Otherwise, I'm fairly confident that in the end, this dog will be able to defeat this cat.
Winner: Iggy