Note: The SSDI, SSI disability system is federal and nationally standardized, though there are state differences in approval rates, wait times, the number of appeals available–as of the time of this writing–and even the name given to the stage disability agency (DDS, or the Bureau or Division of Disability Determination). Now, to answer the question…
Medical records are most of it. But a medical source disability statement from a physician can often make the difference because it supplies a functional assessment that fits neatly with what SSA needs. And medical records very often do not provide this type of clarity.
That said, there are some people who go to hearings unrepresented without doing any preparation other than getting the recent medical records together and do just fine. There are others who do this and get denied while they might have been approved had they been represented.
It would be nice to think that all that is required is just getting your records together so that a totally impartial judge could make the right decision. However, there are many judges who have a ridiculously high rate of denial (just as there are some judges who approve most of their cases). I think considering the fact that some judges seem to automatically lean against claimants, representation at a disability hearing would not be something to arbitrarily dismiss.