Arduino using ESP as shield (AT firmware) is a common topic in this forum… and no need to go through yet another topic with all the diagnostic steps.
As required in the Community Polices, please search thoroughly before asking, as well as reading through all the documentation on this connection method.
http://help.blynk.cc/how-to-connect-different-hardware-with-blynk/arduino/esp8266-with-at-firmware
https://community.blynk.cc/search?q=Arduino%20ESP-01%20shield
Look for proper power options for the ESP, proper pin connection, proper use of the correct Serial methods (Hint, MEGA uses multiple hardware Serial options - no need for Software Serial), etc.
Then, if all else fails… please post the actual code you are using… properly formatted as per those policies in the link above 