Here is the full list of all 22 One-armed cook achievements.
Serve 50 perfect dishes to customers
Serve 100 perfect dishes to customers
Serve 200 perfect dishes to customers
Put out 25 fires
Put out 50 fires
Put out 75 fires
Cook 100 ingredients
Cook 200 ingredients
Cook 500 ingredients
Wash 25 dishes
Wash 50 dishes
Wash 100 dishes
Serve 10 bad dishes
Serve 20 bad dishes
Serve 50 bad dishes
Win 10 games in normal mode
Win 20 games in normal mode
Win 50 games in normal mode
Use 100 ingredients in dishes
Use 200 ingredients in dishes
Use 500 ingredients in dishes
Serve a dish with more than 20 ingredients