Here is the full list of all 13 Chefy-Chef achievements.
Find the Knife for the first time.
Find the Pan for the first time.
Find the Hammer for the first time.
Kill a Frog for the first time.
Kill a Monkey for the first time.
Kill a Croco for the first time.
Collect 10 burgers.
Complete 5 levels.
Complete 15 levels.
Collect 5 burgers.
Collect 15 burgers.
Complete 10 levels.
Complete 20 levels.