There are several ways to check.

Method 1:

function hasKeys(jsonObj, keyList) {
  for (var i=0; i< keyList.length; i++) {
    //if (!jsonObj[0][keyList[i]]) {
    if (!(keyList[i] in jsonObj[0])) {
      return false;
    }
  }
  return true;
}

var keyList = ["Key1", "Key3"];  // array of keys to check if they exists

var str = '[{"Key1":"Value1", "Key2":"Value2","Key3":"Value3","Key4":"Value4"}]';  // json
var jsonObj = JSON.parse(str);

gs.info(hasKeys(jsonObj, keyList));  // check if keys in keyList exists in jsonObj

Methods 2:

function hasKeys2(keys, keyList) {
  return keyList.every(function(val) { return keys.indexOf(val) >= 0; });
}

var keyList = ["Key1", "Key3"];

var str = '[{"Key1":"Value1", "Key2":"Value2","Key3":"Value3","Key4":"Value4"}]';
var jsonObj = JSON.parse(str);
var keys = Object.keys(jsonObj[0]);  // extract all keys from jsonObj

gs.info(hasKeys2(keys, keyList));

Execution:

Case 1: All keys exist

var keyList = ["Key1", "Key2", "Key3"];

var str = '[{"Key1":"Value1", "Key2":"Value2","Key3":"Value3","Key4":"Value4"}]';

Result:

*** Script: true

Case 2: A key does not exist

var keyList = ["Key1", "Key2", "Key3"];

var str = '[{"Key1":"Value1", "Key3":"Value3","Key4":"Value4"}]'; // removed "Key2"

Result:

*** Script: false