Earning the platinum trophy in Kitty Krawler takes about 10 minutes. You simply have to complete the game's 30 levels, all of which are straightforward. The "trick" to the game is that you can only move left, right, and up: you cannot move down unless you knock a grape bunch down, creating a grapevine that you can complete. You must find a path to the cat in the window to complete each level.
There are also some trophies awarded for playing a minigame that occurs around level 20, but those will almost surely come naturally within a few seconds of playing that minigame for the first time.