@dg 
Your desired output contains DG as value for userLabel. I am not sure if it is a typo, so, I tried converting it as well. If not needed, you can remove the modify-overwrite-beta part.

[
  {
    "operation": "modify-overwrite-beta",
    "spec": {
      "userLabel": "DG"
    }
  },
  {
    "operation": "shift",
    "spec": {
      "Types": {
        "*": {
          "subTypes": {
            "*": {
              "*": {
                "$0": "Types[&4].subType[&2].Name",
                "*": {
                  "$": "Types[&5].subType[&3].CounterNames[]",
                  "@": "Types[&5].subType[&3].CounterValues[]"
                }
              }
            }
          },
          "*": "Types[&1].&"
        }
      },
      "*": "&"
    }
  },
  {
    "operation": "shift",
    "spec": {
      "Types": {
        "*": {
          "subType": {
            "*": {
              "CounterNames": {
                "*": "Types[&4].subType[&2].Counters[&].name"
              },
              "CounterValues": {
                "*": "Types[&4].subType[&2].Counters[&].value"
              },
              "*": "Types[&3].subType[&1].&"
            }
          },
          "*": "Types[&1].&"
        }
      },
      "*": "&"
    }
  }
]

Here, the second spec(first shift) gives the following:

{
  "vendor" : "myINC",
  "beginTime" : "2020-01-21T10:00:00+08:00",
  "userLabel" : "DG",
  "Types" : [ {
    "Name" : "type001",
    "subType" : [ {
      "Name" : "subtype003",
      "CounterNames" : [ "counter1", "counter5", "counter54" ],
      "CounterValues" : [ "0", "0", "0" ]
    }, {
      "Name" : "subtype001",
      "CounterNames" : [ "counter002", "counter5", "counter65" ],
      "CounterValues" : [ "0", "0", "0" ]
    } ]
  }, {
    "Name" : "type002",
    "subType" : [ {
      "Name" : "subtype006",
      "CounterNames" : [ "counter1", "counter5", "counter54" ],
      "CounterValues" : [ "0", "0", "0" ]
    }, {
      "Name" : "subtype009",
      "CounterNames" : [ "counter002", "counter5", "counter65" ],
      "CounterValues" : [ "0", "0", "0" ]
    } ]
  } ]
}

The last spec gives you the desired output