Use Serial1 on the Arduino MEGA, instead of using the Software Serial library.

WiFi shield to Arduino MEGA wiring Connection (for Diagram Please see the Attachments file below)

• GND ---> GND • D2 ---> D19 • D3 ---> D18

The Sample Sketch: https://www.e-gizmo.net/oc/kits%20documents/ESP-11%20wifi%20shield/Sample%20Code.zip