This is for finishing the game without dying. This must be done in story mode and can't be done in Free Play by just re-doing the levels you did not die on. Recommended to change the difficulty to easy for this. To check if you have died or not you can Pause the game and go to Stats where it should say "Times caught 0".UPDATE: Thanks to I ASK NO ONE for pointing this out. The stat actually is cumulative. The recommendation is to delete your save completely and start over or go for this one first so that it's easy to keep track of your "times caught". I believe the achievement will still unlock as long as the times caught counter does not increase. For example, if you started with times caught at 5, if you finish the game with it still saying 5, the achievement should unlock.
There are a few ways to "die" in this game. If you see a death coming, you can quickly hit pause and load last checkpoint. If you do actually die, you can delete local save and load up the cloud save. Done by going to game's save management and deleting it from local only. (DO NOT hit delete everywhere or delete cloud save) This will reset back progress about 2-3 minutes but it's better having to re-do the entire game because of one death.
- Get caught in the lawnmower in Home Sweet Home for Trim Your Moustache achievement.
- Get caught by the chef in the grocery store.
- Get discovered by the marine scientists in the Aquarium. (This can't happen on easy)
- Fall overboard in the Sea Legs level.
- Get caught by the chef, fall in the fire, get hit with a cleaver in the last level.
Here's a video guide in 3 parts going as fast as possible without doing any of the unrequired stuff. Difficulty is set to easy so some of the things done in this video may not be the same if you set difficult to something else.