As someone who loves Call of Duty: Modern Warfare 3's Spec-Ops Survival mode, these two achievements were earned pretty early on for me. But if you need some pointers, let this great tutorial drop some science. Basically, you have to reach waves 10 and 15 on any map in Survival.
The 'Survivor' achievement will get you 20G on Xbox 360, and a silver trophy on PlayStation 3. If you manage to get 'Unstoppable', that's good for 40G on Xbox 360, and a silver trophy on Playstation 3.