Set the difficulty to easy. This makes it so, with the exception of specific hazards (the chef in his second and final appearances, the toilet biologist in the penultimate level, the fires at the very end, etc.), suspicion won't increase regardless of what you do. Then, start a new game. From that point on, just clear every level. The game is already incredibly easy even before dropping the difficulty, so unless you stuff up on one of the few hazards that can end your run, you should be able to get this achievement within 10-15 minutes.