You may find this link to be of interest.
In essence, what you need to do is to distinguish between the "actual" coordinates, and the "display" coordinates of each object.
What you would do is do the bulk of the work using the actual coordinates of each entity in your game. If it helps, imagine that you have a gigantic screen that can show everything at once, and calculate everything as normal. It might help if you also designed the camera to be an entity, so that you can update the position of your camera just like any other object.
Once everything is updated, you go to the camera object, and determine what tiles, objects, particles, etc. are visible within the window, and convert their actual, world coordinates to the pixel coordinates you need to display them correctly.
If this is done correctly, you can also do things like scale and otherwise modify the image your camera is displaying without affecting gameplay.
In essence, you want to have a very clear distinction between gameplay and physics logic/code, and your rendering/display code, so your game can do whatever it wants, and you can render it however you want, with minimal crossover between the two.
So the good news is, you probably don't need to change anything about how your game itself works. The bad news is, you'll probably have to go in and rewrite your rendering/drawing code so that everything is drawn relative to the camera, not to the world.