2013 300h 12v Battery
 

I think my 12V battery in the trunk is dying. Can I replace the battery with a regular battery you buy at Auto Part Stores. No one has a parts listing for a 300H

If I were you I would stick with the AGM battery the car came with even if it was more expensive, for the following reason
The battery location in the trunk where you put your grocery and luggage makes regular battery not the best choice.
The AGM battery is sealed spill proof battery with a venting port on one side to make sure any acid vapor is vented to the outside and not in the trunk. Plus the battery has very limited space in the right corner of the trunk, so you have to find battery with similar dimensions.
A regular battery may work, but I don't want it next to my grocery and clothes

I was speaking with a shop and they were mentioning some batteries don't play nice with smartcars...

Have you had your battery tested. Our here you can have it done at the local auto parts store for free..