Is ESD protection necessary on a battery powered device?
What kind of ESD protection is typically required/recommended when
  designing battery powered electronics?


Many modern IO chips will state the ESD human body level withstand voltage in their data sheets and you could use that figure. It makes no difference that the unit is battery powered or not - the IO chips most vulnerable do not know this and cannot change their protection characteristics!

Next, you have to decide what human body model ESD voltage level is suitable for your product. 

Some chips will be 4 kV suitable but (for instance), you might want to go for 8 kV then you have to decide whether to change the chips or apply supplementary protection.

If you go for supplementary protection then several different methods may be suitable. For inputs adding a series resistor and TVS/zener is usually enough and some inputs may be OK with ESD diodes direct to the internal power rails. Just adding a capacitor from input to 0V may sometimes be good enough.

Outputs are generally required to drive more current and may not be so easily protected in the same way as inputs so, without getting into a long-drawn out series of guesses, I suggest you come clean and spill the details.