After the opening tutorial level and cutscene you'll make your way to the Warp Room. Cortex will ask you to gather Purple Crystals for him. Simply play the first level, Turtle Woods, and intentionally miss the first Purple Crystal in the game.
Do this twice. Play the entirety of Level 1 without acquiring the level's very obvious Crystal. Cortex will become irate and yell at Crash a second time, unlocking the Trophy. To my knowledge this only works at the very beginning of a playthrough.
Note: Acquiring the level's Blue Gem by finishing the level without breaking any boxes does not negatively affect this Trophy. However, breaking all boxes and earning the game's first Silver Gem does trigger a different cutscene, which may affect this Trophy from unlocking.
Edit: According to users Stu003 and AtomHeartFylus, you can simply start the level and immediately Exit to the Warp Room three times for the Trophy to unlock. Thanks for the information!