Hello,
Some basic info that should cover most vehicles -- certainly does not indicate the Cobalt's individual specifications, but will get you into the ballpark:
A battery without the engine running should have voltage of around 12.5 to 12.7, fully charged. With a load applied to the proper cold cranking amp rating of the battery, it should not fall below 10.5 volts or so, and should stay steady for a period of several seconds.
The alternator should come close to producing the specified amperage for the vehicle when loaded at 2,000 RPM engine speed. With your 2.2L 4 cylinder engine, you could peak at 80 amps when loaded.
The voltage regulator voltage should usually be at bare minimum above 13.8 volts. This again could vary by model specification. but at 13.5 volts, i'd be concerned about a diode issue in the alternator / voltage regulator.
Check the wiring connector at the alternator to ensure all terminals are intact and the connector is not melted or compromised in any ways.
Testing with the proper equipment and seeking the voltage and amperage as needed will yield you the answer you are seeking.
