Hi,
You need better power for sure...
The servos need 5 to 6 volts at perhaps 1 to 2 amps. So separate external power supply is needed. 5V to servos, external power supply ground connected to Arduino ground.
For the arduino, separate power. Wall wart of equivalent, like 9V 1A to external power.
the 9V alkaline won't work.
You MAY be able to use 4 AA NiMH batteries to run both Arduino 5V and the servos.