High voltage/Mid current boost converter
frankly if your not familiar with power supply design you shouldn't be starting with generating dangerous voltages.  Additionally i assume your listed outputs are DC given that the part you listed is a DC-DC converter.

+60V DC will penetrate your skin (not to speak of -108 or -120).  It takes &lt;100mA of current through your heart to send it into fibrillation.  Which you could easily do with +60V, dry skin and getting +vdd on one hand and GND on the other, wet skin is far worse. 

All that aside what you need is a DC to DC boost converter controller with invert for the negative voltages and external switching transistors that can handle the voltage.

You should build a few low voltage designs using this topology so you fully understand it before you attempt to create what your asking for.