I have a collection of DLLs(say 20). How do I find out all the DLLs on which one specific DLL (say DLL A) is depending upon?
Since the question is tagged "C#", I would assume you are talking about managed dlls (assemblies). In that case, dependencywalker is not useful. If you want to do that with a program, good ones are dotPeek by JetBrians and Reflector by RedGate. Or you can even use the object inspector in Visual Studio.
However, it can be a long process and cumbersome too. I would write a short C# program/F# script that uses Assembly.GetReferencedAssemblies, as Jon mentioned.
If instead you want to examine native DLLs dependencies with a program (C# code), you have to walk the examine the PE file (the MS dll and exe file format) and its IAT (import address table). Not easy, but not impossible...
I would start here on MSDN and here to understand PE sections, and use a managed library to read it (there are many, including some from the Mono project (I'm thinking of Cecil, it should work with native binaries too); in the past I have used this one from the good John Gough.