Arduino dies when I use a 3.3v regulator

An Arduino should easily be capable of powering a single regulator and nRF24L01 module. The nRF24 chip takes 13.5 mA at worst case consumption. I'm betting something is miswired. Been a while since I used an nRF24 though.

nRF24L01 has 5V tolerant inputs. Level translation is not necessary for this chip.