The Hero of Thyme trophy in Overcooked! is story-related and can't be missed, although reaching this far will likely need lots of coordination with your local co-op partner.
The trophy will unlock after you complete all six of the game's worlds, and finish the final level against the giant meatball monster.
Below is a video of the final boss fight so that you can get an idea of how difficult it can be (credit to aallawi2 on YouTube):