To acquire the Lost Crown of Genghis Khan and net this achievement, you have to defeat the boss at the end of the Himalayas level on any difficulty. To defeat the boss you have to dodge the ice blocks that she causes to rain down on you. Among the ice blocks will be a single stone. Use the stone to knock a large ice block down on her head that will cause her to sink in the snow, then pogo on her head. Repeat until she's done. You will likely have to run underneath her as well when she is jumping. Time this right and you can make it. Occasionally she will jump and shake while in the air. When this happens you have to jump just before she hits the ground or you will be hurt. Once defeated, a cut scene will start and you will the get the crown. The achievement pops once you are back in your vault headquarters.