Battery problems

I'm no expert but usually feel like i have a good enough grasp on vehicles. Friend of mine is having some battery problems and was wondering if anyone could tell me if it's more then that.
Battery wont hold a charge once turned off and has started giving off an eggy smell.
there are some wet looking marks around the seam of the battery but i haven't seen any active leaks and even the spots feel totally dry. nothing of note other then that has been happening. my diagnosis was "get a new battery" but the internet has been telling me broken alternator (which i don't know how to fix) was hoping someone else may have some advice before i buy a battery or an alternator or both.