It is most likely that you will want to document your trek up the mountains with lots of pictures so here are some tips to consider in looking after your camera and getting the most out of your photos.
Whether you're using a fully automatic 'point and shoot' camera (which is what most people do) or you're taking your DSLR camera with you so you can get those more professional shots, you'll want to make sure you have enough batteries. Remember, there's no electricity on the mountain so you will not be able to charge up your batteries until you return to civilisation below! Battery life is also much shorter in freezing conditions so make sure you have sufficient batteries to carry you through your entire journey.
You will also be climbing from the tropics to high altitudes (likely below 32*f) and the climate changes will potentially affect your camera. Although the camera should still work fine when exposed to the cold, if you keep your camera warm inside your jacket, the chances are the lens will be covered in condensation and will freeze once it's exposed to the cold conditions at the summit. If that happens, then you camera will stop functioning so be sure to keep your camera dry!
Bring a waterproof container (or ziploc bags) to protect your camera, lenses, etc. As well as keeping them dry, this will protect them from the dust and dirt. Also, make sure your camera is fully set up for taking pictures once you reach the summit. You don't want to be messing with lens changes at that time. If you're concerned about your primary camera not functioning when you want it most, consider taking a back-up camera to make sure you can capture your accomplishment.