In the very first campaign mission, there is a part where Peter tells you swap places with him to take care of Rhino. Right after that, Rhino jumps into a parking garage and proceeds into a mall. From this point until the JJJ studio cutscene is the portion of the game where you rack up credit toward this achievement.
When accounting for Rhino's movement speed, the placement of obstacles, and the areas where you simply don't get to control Rhino, there are only 10 things you can smash into when completing this sequence and it is not possible to complete this trophy on your first try.
However, even though the game never tells you, mission select is unlocked when you complete the campaign and you can replay this level to smash more stuff. It's annoying to go through the entire intro cutscene and tutorial that leads up to this Rhino sequence, but it's much better than starting new game plus playthroughs 2 or 3 times. Just hit the touchpad to open up the in-game menu, go to Missions, and select the mission to replay.
I'm also positive this tracks on the entire profile between all saves. I played through the game once for 100%, did a couple campaign missions on new game plus, then went back to my original 100% save (because I couldn't mission select on new game plus) and only smashed 2 things for the trophy. What this tells me is that I needed more than 2 things at the time of starting new game plus, otherwise the trophy would have unlocked at that time.