Circuit Design to Power the ADH8066 GSM Module
You are saying that the device requires 4V and bursts of current up to 2A, and that your Arduino isn't capable of supplying that.  So don't try to make it.

Either get a separate power supply for each device, or a bigger beafier one that can handle both.  I don't know what voltage the Arduino wants, so I'll assume 5V.  Get a 2.5A or more 5V supply, power the Arduino from it directly, and power the GSM module from it with a 4V LDO regulator.