This trophy could very well be a runner up for the hardest in the game IF I hadn't found an exploit for it. Simply go into any mini-game or Puzzle that takes place at night and complete it. It's as easy as that. I personally didn't expect it to pop, but it does. If you're the adventurous type and want to get it legit, than the easiest would be the first night level during your 2nd Adventure run (2-1).
Just like my other tactics, I suggest placing 2-3 sunflowers to start. Once a zombie spawns place a Potato Mine on the same path and continue placing Sunflowers. Once you have enough start building your peashooters. I also suggest having Snow Peas and wall-nuts for this.