Replacing the alternator on the Kia Rio is probably one of the most difficult work I have done, which is a strange thing to say because I have done far more complex tasks on this vehicle. Even though it is relatively easy to disconnect the belts and remove all the retaining bolts, there is simply no room to extricate the alternator out of the engine.
At the top, the path is blocked by the AC lines and the power steering lines. At the bottom, the the mounting block obstructs the path.
After checking many sources of information, the only apparent way to get it out was by lifting and moving the engine. This clearly seems like a poor design and unnecessarily complicated.
Therefore, passenger-side engine mount was removed, letting the engine hang from the other mount points. Then a hydraulic jack was placed under the oil pan to lift the engine block. This procedure moved the engine by about an inch, and allowed the alternator to just barely squeeze out of the bottom of the vehicle with no extra room to spare.