The first level, "Land of Chocolate", is the easiest to gain this achievement on. You will have to repeatedly fall into the chocolate.
You only "die" when Nelson comes up and says, "Ha-ha". Falling into the chocolate does not kill you, it only takes away some of your health. I had to fall into the chocolate 4 times to actually "die". Repeat 9 additional times.
On others levels, both characters must "die".
This is across the entire game too. You don't have to do it in one level or in one sitting.