By diversifying your tiles you can not only mitigate the damage done by targeting your tiles, but prevent them from being such a large target in the first place.
There are a few ways to avoid, or at least mitigate, the damage done by the robber. The first is by not putting all of your eggs in one basket. You should not build settlements where one of the tiles is great and the other tiles are mediocre, because if the robber is placed on your great tile it can basically shut down the production of that settlement. This can be especially devastating if you build cities or multiple settlements around a single great tile, which basically turns this tile into a huge glowing target. By diversifying your tiles you can not only mitigate the damage done by targeting your tiles, but prevent them from being such a large target in the first place.