For a battery powered by electrochemistry, there will be a natural limit on its energy density of the following form:
Batteries work by capturing and diverting the electron transfers occurring in chemical reactions that happen in solution (commonly). This means that a chunk of, say, zinc metal in a zinc-copper battery has a certain number of charge units (of electrons) which it releases at a certain voltage. the charge transfer is current and current times voltage is power; divide by the density of zinc and now you have some number which represents the maximum theoretical electrochemical power density of zinc metal on a per-kilogram basis.
To fully exploit that power density requires the invention of a battery consisting almost entirely of replaceable chunks of zinc metal and an electrochemical reaction with no resistive losses- neither of which are possible today.