If you have the tiles seperated in different layers as render targets, you could just blur those with gaussian blur for example. There should be lots of examples online how to do gaussian blur. Preferrably you would do this in two passes, one horizontal and one vertical in arbitrary order. This leads to the exact same result but reduces computational cost.
The effect I use is Depth of Field. It uses the depth to decide how blurry it should get. So it should be viable also for 2D, provided you have access to the depth like @kosmonautgames mentioned.
One method to implement DoF, is to blur the image. Then in the next step, depending on the depth, you could sample the non-blurred or blurred version of the image.
I used a more advanced technique, where focused image regions also stay focused if there is an adjacent out-of-focus image region. Maybe this isn't clearly visible in the image due to lacking time to find better parameter values, to make the transition region from focused to non-focused more sharp.