How do I amplify a square wave pulse of 4 to 8 periods at 3.5 MHz from +-2V to +-60V or more?
You want to drive a capacitive transducer at 3.5MHz with 120Vp-p, which is a fairly tall order. The peak power is rather high (3A peak at 60V). 

You can purchase high-voltage power op-amps, some of which have example circuits that show driving heavily capacitive loads. I've done a discrete booster amplifier for driving piezos, but it's tricky to get it to work in a stable manner with that kind of heavy capacitive load.