Hum, if you research transformer designs without iron cores, you will get some idea on how the transformer should be. But believe me, you probably need to make a different couple of designs and try them out.
on the primary side, you need some kind of switching to get the transfer, on the secondary side you need some sort of rectifier circuit, and lipo charger circuit.
If I was to going to do this, I would take a look on a SMPS chip, and use this as the primary switching side.