I used to be able to connect a dualshock to my Note 3, and I remember it being pretty bang simple. PS2 Dualshocks use Bluetooth. But maybe the modern Bluetooth protocol is incompatible, I haven't tried with my newer phones.
Edit: Ah wait, I'm remembering wrong. I used a dualshock 3, like for the PS3. Those ones use Bluetooth. Not sure about the wireless dualshock 2s. They might use some proprietary 2.4GHz connection.