Japanese cold soba broth? I remember having been in Japan and ate several meals of cold soba. Their cold soba broth taste like soy sauce with only a stint of saltiness; it doesn't taste like it's made of sushi type sweetened soy sauce; neither does it taste like a simple mixture of soy sauce and water. 

Instead of using pre-made cold soba broth, I want to replicate these Japanese cold soba broth at home.  Googling directs me to different recipes: some suggest mixing soy sauce with chicken broth (I can't recall any stock-ish taste); some suggest mixing with Mirin (alcohol in a soba broth - I don't think so..).

Does any know how to make cold soba broth or at least know the essential ingredients?
The basis for any sort of Japanese soup dish is going to be dashi stock, a stock made of fish and seaweed. It has a much lighter flavor than chicken broth, so you might not have identified it easily. You can buy it in a powder form for convenience, and it can be sprinkled into other liquids rather than reconstituted. 

This recipe is for soba with a dipping sauce, but it'll give you a good idea of the flavor profile you're looking for: Dashi stock plus kaeshi, which is made of soy sauce, mirin, and sugar (and simmered so it's not strongly alcoholic).