To unlock the Here Kitty-Kitty trophy in Spider-Man The City That Never Sleeps: The Heist, simply progress through the main campaign until you get to a point where you are chasing Cat across the rooftops.
Like many chases in the main game you need to stay in range for a couple of seconds (about 20 metres or less) until you get a button prompt. However this isn't a simple
job; you need to spam R1 and keep webbing Cat up until eventually you can strike with
. You'll naturally slow down a bit each time you tag her with
so this will take a few rounds of chasing and striking before she is weakened enough to strike. As soon as you wrap up the rest of the mission the trophy will unlock.